GEORESOURCES, INC. WARRANT TO PURCHASE SHARES OF COMMON STOCK, PAR VALUE $0.01 PER SHARE

Exhibit 10.34

THE SECURITIES REPRESENTED HEREBY MAY NOT BE TRANSFERRED UNLESS (I) SUCH SECURITIES HAVE BEEN REGISTERED FOR SALE PURSUANT TO THE SECURITIES ACT OF 1933, AS AMENDED, (II) SUCH SECURITIES MAY BE SOLD PURSUANT TO RULE 144 WITHOUT RESTRICTION, OR (III) THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO IT THAT SUCH TRANSFER MAY LAWFULLY BE MADE WITHOUT REGISTRATION UNDER THE SECURITIES ACT OF 1933 OR QUALIFICATION UNDER APPLICABLE STATE SECURITIES LAWS. NOTWITHSTANDING THE FOREGOING, THE SECURITIES MAY BE PLEDGED IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT OR OTHER LOAN OR FINANCING ARRANGEMENT SECURED BY THE SECURITIES PROVIDED THAT SUCH PLEDGE DOES NOT CONSTITUTE OR RESULT IN A TRANSFER OF THE SECURITIES UNDER ANY APPLICABLE LAWS, RULES OR REGULATIONS.

No.                     

GEORESOURCES, INC.

WARRANT TO PURCHASE              SHARES OF

COMMON STOCK, PAR VALUE $0.01 PER SHARE

For VALUE RECEIVED,              (“ Warrantholder ”), is entitled to purchase, subject to the provisions of this Warrant, from GEORESOURCES, INC. , a Colorado corporation (“ Company ”), at any time not earlier than the date that is six months after the date hereof (the “ Initial Exercise Date ”) and not later than 5:00 P.M., Eastern time, on June 9, 2013 (the “ Expiration Date ”), at an exercise price per share equal to $32.43 (the “ Exercise Price ”),              shares (“ Warrant Shares ”) of the Company’s Common Stock, par value $0.01 per share (“ Common Stock ”). The number of Warrant Shares purchasable upon exercise of this Warrant and the Exercise Price shall be subject to adjustment from time to time as described herein.

Section 1. Registration . The Company shall maintain books for the transfer and registration of this Warrant. Upon the initial issuance of this Warrant, the Company shall issue and register this Warrant in the name of the Warrantholder.

Section 2. Transfers . As provided herein, this Warrant may be transferred only pursuant to a registration statement filed under the Securities Act of 1933, as amended (the “ Securities Act ”), or an exemption from such registration. Subject to such restrictions, the Company shall transfer this Warrant from time to time upon the books to be maintained by the Company for that purpose, upon surrender thereof for transfer, properly endorsed or accompanied by appropriate instructions for transfer and such other documents as may be reasonably required by the Company, including, if required by the Company, an opinion of its counsel to the effect that such transfer is exempt from the registration requirements of the Securities Act, to establish that such transfer is being made in accordance with the terms hereof, and a new Warrant shall be issued to the transferee and the surrendered Warrant shall be canceled by the Company.

Section 3. Exercise of Warrant .

(a) This Warrant may be exercised in whole or in part at any time on or after the Initial Exercise Date and prior to the Expiration Date upon delivery of the notice of exercise form attached hereto as Appendix A (the “ Notice of Exercise ”) and payment by cash, certified check or wire transfer (or, in certain circumstances, by cashless exercise as provided in Section 3(d) ) for the aggregate Exercise Price for that number of Warrant Shares then being purchased, to the Company during normal business hours on any day other than a Saturday or Sunday on which banks are open for business in New York City (a “ Business Day ”) at the Company’s principal executive offices (or such other office or agency of the Company as the Company may designate by notice to the Warrantholder). The Warrant Shares so purchased shall be deemed to be issued to the Warrantholder or the Warrantholder’s designee, as the record owner of such shares, as of 5:00 P.M. New York City time on the date on which the aggregate Exercise Price shall have been paid and the completed Notice of Exercise shall have been delivered. Certificates for the Warrant Shares so purchased, representing the aggregate number of shares specified in the Notice of Exercise, shall be transmitted by the Company’s transfer agent by crediting the account of the Warrantholder’s prime broker with The Depository Trust Company (“ DTC ”) through its Deposit / Withdrawal At Custodian (“ DWAC ”) system if the Company is a participant in such system, and otherwise by physical delivery to the address specified by the Warrantholder in the Notice of Exercise, within a reasonable time, not exceeding three (3) Trading Days (as defined below) after this Warrant shall have been so exercised, including payment of the aggregate Exercise Price and the delivery of a completed Notice of Exercise (the “ Warrant Share Delivery Date ”). The certificates so delivered shall be in such denominations as may be requested by the Warrantholder and shall be registered in the name of the Warrantholder or such other name as shall be designated by the Warrantholder in the Notice of Exercise. In addition to any other rights available to the Warrantholder, if the Company fails to deliver to the Warrantholder a certificate or certificates representing the Warrant Shares pursuant to an exercise on or before this Warrant Share Delivery Date, and if after such date the Warrantholder is required by its broker to purchase (in an open market transaction or otherwise) shares of Common Stock to deliver in satisfaction of a sale by the Warrantholder of the Warrant Shares which the Warrantholder anticipated receiving upon such exercise (a “ Buy-In ”), then the Company shall either (i) pay cash to the Warrantholder in an amount equal to the Warrantholder ‘s total purchase price (including brokerage commissions, if any) for the shares of Common Stock so purchased (the “ Buy-In Price ”), at which point the Company’s obligation to deliver such certificate (and to issue such shares of Common Stock) or credit such Holder’s balance account with DTC shall terminate, or (ii) promptly honor its obligation to deliver to the Warrantholder a certificate or certificates representing such shares of Common Stock or credit such Warrantholder’s balance account with DTC and pay cash to the Warrantholder in an amount equal to the excess (if any) of the Buy-In Price over the product of (A) such number of shares of Common Stock, times (B) the Closing Bid Price on the date of exercise. Warrantholder shall provide the Company written notice indicating the amounts payable to the Warrantholder in respect to the Buy-In, together with applicable confirmations and other evidence reasonably requested by the Company. Nothing herein shall limit a Warrantholder’s right to pursue any other remedies available to it hereunder, at law or in equity including, without limitation, a decree of specific performance and/or injunctive relief with respect to the Company’s failure to timely deliver certificates representing shares of Common Stock upon exercise of this Warrant as required pursuant to the terms hereof. Notwithstanding anything herein to the contrary, the Warrantholder shall not be required to physically surrender this Warrant to the Company until

2

the Warrantholder has purchased all of the Warrant Shares available hereunder and this Warrant has been exercised in full, in which case, the Warrantholder shall surrender this Warrant to the Company for cancellation within three (3) Trading Days of the date the final Notice of Exercise is delivered to the Company. Partial exercises of this Warrant resulting in purchases of a portion of the total number of Warrant Shares available hereunder shall have the effect of lowering the outstanding number of Warrant Shares purchasable hereunder in an amount equal to the applicable number of Warrant Shares purchased. The Warrantholder and the Company shall maintain records showing the number of Warrant Shares purchased and the date of such purchases. The Company shall deliver any objection to any Notice of Exercise Form within one Business Day of receipt of such notice. In the event of any dispute or discrepancy, the records of the Company’s transfer agent shall be controlling and determinative in the absence of manifest error. The Warrantholder and any assignee, by acceptance of this Warrant, acknowledge and agree that, by reason of the provisions of this paragraph, following the purchase of a portion of the Warrant Shares hereunder, the number of Warrant Shares available for purchase hereunder at any given time may be less than the amount stated on the face hereof. For purposes of this Warrant (i) a “ Trading Day ” means (A) a day on which the Common Stock is traded on a Trading Market (as defined below), or (B) if the Common Stock is not listed on a Trading Market, a day on which the Common Stock is traded on the over the counter market, as reported by the National Association of Securities Dealers, Inc. OTC Bulletin Board (the “ Bulletin Board ”), or (C) if the Common Stock is not quoted on the Bulletin Board, a day on which prices for the Common Stock are reported in the Pink Sheets published by Pink Sheets LLC (or any similar organization or agency succeeding to its functions of reporting prices); provided, that in the event that the Common Stock is not listed, quoted or reported as set forth in (A), (B) and (C) hereof, then Trading Day shall mean a Business Day and (ii) “ Trading Market ” means the following markets or exchanges on which the Common Stock is listed or quoted for trading on the date in question: the NASDAQ Global Select Market, the NASDAQ Global Market, The NASDAQ Capital Market, the American Stock Exchange or the New York Stock Exchange.

In addition to any other rights available to the Warrantholder, if the Company fails to deliver to the Warrantholder a certificate or certificates representing the Warrant Shares pursuant to an exercise on or before the Warrant Share Delivery Date, the Company shall be liable to the Warrantholder for liquidated damages in an amount equal to 1.5% of the aggregate Exercise Price of the Warrant Shares issuable pursuant to such exercise for each thirty (30) day period (or pro rata for any portion thereof) beyond the Warrant Share Delivery Date.

(b) If this Warrant shall have been exercised in part, the Company shall, at its own expense and at the time of delivery of the certificate or certificates representing Warrant Shares, deliver to the Warrantholder a new Warrant evidencing the rights of the Warrantholder to purchase the unpurchased Warrant Shares called for by this Warrant, which new Warrant shall in all other respects be identical to this Warrant.

(c) Notwithstanding anything to the contrary herein, the Warrantholder shall not have the right to exercise any portion of this Warrant, pursuant to Section 3 or otherwise, to the extent that after giving effect to such issuance after exercise, the Warrantholder (together with the Warrantholder’s affiliates), as set forth on the applicable Notice of Exercise, would beneficially own in excess of 4.99% of the number of shares of the Common Stock outstanding immediately after giving effect to such issuance. For purposes of the foregoing sentence, the

3

number of shares of Common Stock beneficially owned by the Warrantholder and its affiliates shall include the number of shares of Common Stock issuable upon exercise of this Warrant with respect to which the determination of such sentence is being made, but shall exclude the number of shares of Common Stock which would be issuable upon (A) exercise of the remaining, nonexercised portion of this Warrant beneficially owned by the Warrantholder or any of its affiliates and (B) exercise or conversion of the unexercised or nonconverted portion of any other securities of the Company (including, without limitation, any other shares of Common Stock or Warrants) subject to a limitation on conversion or exercise analogous to the limitation contained herein beneficially owned by the Warrantholder or any of its affiliates. Except as set forth in the preceding sentence, for purposes of this Section 3(c) , beneficial ownership shall be calculated in accordance with Section 13(d) of the Exchange Act, it being acknowledged by the Warrantholder that the Company is not representing to the Warrantholder that such calculation is in compliance with Section 13(d) of the Exchange Act and the Warrantholder is solely responsible for any schedules required to be filed in accordance therewith. For purposes of this Section 3(c) , in determining the number of outstanding shares of Common Stock, the Warrantholder may rely on the number of outstanding shares of Common Stock as reflected in the latest of (x) the Company’s most recent Form 10-Q or Form 10-K, as the case may be, (y) a more recent public announcement by the Company or (z) any other notice by the Company or the Company’s transfer agent setting forth the number of shares of Common Stock outstanding. Following the written or oral request of the Warrantholder, the Company shall, or shall cause its transfer agent to, within two Trading Days confirm orally and in writing to the Warrantholder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or exercise of securities of the Company, including this Warrant, by the Warrantholder or its Affiliates since the date as of which such number of outstanding shares of Common Stock was reported. The provisions of this Section 3(c) may be waived by the Warrantholder, at the election of the Warrantholder, upon not less than 61 days’ prior notice to the Company, and the provisions of this Section 3(c) shall continue to apply until such 61st day (or such later date, as determined by the Warrantholder, as may be specified in such notice of waiver).

(d) Notwithstanding any other provision contained herein to the contrary, so long as the Company is required under the Registration Rights Agreement dated as of June 5, 2008 among the Company and the investors party thereto (the “ Registration Rights Agreement ”) to have effected the registration of the Warrant Shares for sale to the public pursuant to a Registration Statement (as such term is defined in the Registration Rights Agreement), if the Warrant Shares may not be freely sold to the public for any reason (including, but not limited to, the failure of the Company to have effected the registration of the Warrant Shares, the failure to have a current prospectus available for delivery or otherwise, or during the period of any Allowable Grace Period (as defined in the Registration Rights Agreement)), the Warrantholder may elect to receive, without the payment by the Warrantholder of the aggregate Exercise Price in respect of the shares of Common Stock to be acquired, shares of Common Stock equal to the value of this Warrant or any portion hereof by the surrender of this Warrant (or such portion of this Warrant being so exercised) together with the Net Issue Election Notice annexed hereto as Appendix B duly executed, at the office of the Company. Thereupon, the Company shall issue to the Warrantholder such number of fully paid, validly issued and nonassessable shares of Common Stock as is computed using the following formula:

4

X = Y (A - B)

A

where

X = the number of shares of Common Stock which the Warrantholder has then requested be issued to the Warrantholder;

Y = the number of Warrant Shares covered by this Warrant that the Warrantholder is surrendering at such time for cashless exercise (including both shares to be issued to the Warrantholder and shares to be canceled as payment therefor);

A = the Market Price (as defined below) of one share of Common Stock as at the time the net issue election is made; and

B = the Exercise Price in effect under this Warrant at the time the net issue election is made.

Section 4. Compliance with the Securities Act of 1933 . If the Registration Statement is not effective at any time that this Warrant is exercised, (i) the Warrant Shares issued upon such exercise shall be “restricted securities,” (ii) the stock certificate evidencing the Warrant Shares shall bear a restrictive legend set forth on the first page of this Warrant unless counsel to the Company is of the opinion that such legend is not necessary. In addition, as a condition precedent to issuance of the Warrant Shares upon such exercise, the Warrantholder shall be required to execute an investment representation statement in the form provided by the Company as evidence of the Warrantholder’s qualifications to purchase Common Stock in a “private placement” that is exempt from registration pursuant to Section 4(2) of the Securities Act.

Section 5. Payment of Taxes . The Company will pay any documentary stamp taxes attributable to the initial issuance of Warrant Shares issuable upon the exercise of this Warrant; provided, however, that the Company shall not be required to pay any tax or taxes which may be payable in respect of any transfer involved in the issuance or delivery of any certificates for Warrant Shares in a name other than that of the Warrantholder in respect of which such shares are issued, and in such case, the Company shall not be required to issue or deliver any certificate for Warrant Shares or any Warrant until the person requesting the same has paid to the Company the amount of such tax or has established to the Company’s reasonable satisfaction that such tax has been paid. The Warrantholder shall be responsible for income taxes due under federal, state or other law, if any such tax is due.

Section 6. Mutilated or Missing Warrants . In case this Warrant shall be mutilated, lost, stolen, or destroyed, the Company shall issue in exchange and substitution of and upon cancellation of the mutilated Warrant, or in lieu of and substitution for this Warrant lost, stolen or destroyed, a new Warrant of like tenor and for the purchase of a like number of Warrant Shares, but only upon receipt of evidence reasonably satisfactory to the Company of such loss, theft or destruction of this Warrant, and with respect to a lost, stolen or destroyed Warrant, reasonable indemnity or bond with respect thereto, if requested by the Company.

5

Section 7. Reservation of Common Stock . The Company hereby represents and warrants that there have been reserved, and the Company shall at all applicable times keep reserved until issued (if necessary) as contemplated by this Section 7 , out of the authorized and unissued shares of Common Stock, sufficient shares to provide for the exercise of the rights of purchase represented by this Warrant. The Company agrees that all Warrant Shares issued upon due exercise of this Warrant shall be, at the time of delivery of the certificates for such Warrant Shares, duly authorized, validly issued, fully paid and non-assessable shares of Common Stock of the Company.

Section 8. Adjustments . The Exercise Price and number of Warrant Shares subject to this Warrant shall be subject to adjustment from time to time as set forth in this Section 8 .

(a) If the Company shall, at any time or from time to time while this Warrant is outstanding, pay a dividend or make a distribution on its Common Stock in shares of Common Stock, subdivide its outstanding shares of Common Stock into a greater number of shares or combine its outstanding shares of Common Stock into a smaller number of shares or issue by reclassification of its outstanding shares of Common Stock any shares of its capital stock (including any such reclassification in connection with a consolidation or merger in which the Company is the continuing corporation), then the number of Warrant Shares purchasable upon exercise of this Warrant and the Exercise Price in effect immediately prior to the date upon which such change shall become effective, shall be adjusted by the Company so that the Warrantholder thereafter exercising this Warrant shall be entitled to receive the number of shares of Common Stock or other capital stock which the Warrantholder would have received if this Warrant had been exercised immediately prior to such event upon payment of an Exercise Price that has been adjusted to reflect a fair allocation of the economics of such event to the Warrantholder. Such adjustments shall be made successively whenever any event listed above shall occur.

(b) If any capital reorganization, reclassification of the capital stock of the Company, consolidation or merger of the Company with another corporation in which the Company is not the survivor, or sale, transfer or other disposition of all or substantially all of the Company’s assets to another corporation shall be effected (each, a “ Fundamental Transaction ”), then, as a condition of such Fundamental Transaction, lawful and adequate provision shall be made whereby each Warrantholder shall thereafter have the right to exercise this Warrant and receive upon the basis and upon the terms and conditions herein specified and in lieu of the Warrant Shares immediately theretofore issuable upon exercise of this Warrant, such shares of stock, securities or assets as would have been issuable or payable with respect to or in exchange for a number of Warrant Shares equal to the number of Warrant Shares immediately theretofore issuable upon exercise of this Warrant, had this Warrant been exercised in full immediately prior to such Fundamental Transaction (the “ Transaction Consideration ”), and in any such case appropriate provision (as determined in good faith by the Board of Directors of the Company) shall be made with respect to the rights and interests of each Warrantholder to the end that the provisions hereof (including, without limitation, provision for adjustment of the Exercise Price) shall thereafter be applicable, as nearly equivalent as may be practicable in relation to any Transaction Consideration deliverable upon the exercise hereof. The Company shall not effect any such Fundamental Transaction unless prior to or simultaneously with the consummation thereof the successor corporation or entity (if other than the Company) resulting from such

6

consolidation or merger, or the corporation or entity purchasing or otherwise acquiring such assets or other appropriate corporation or entity shall assume the obligation to deliver to the Warrantholder, at the last address of the Warrantholder appearing on the books of the Company, such Transaction Consideration as, in accordance with the foregoing provisions, the Warrantholder may be entitled to receive upon exercise hereof, and the other obligations under this Warrant. Without limiting the generality of the foregoing, the terms of any agreement pursuant to which a Fundamental Transaction is effected shall include terms requiring any such successor or surviving entity to comply with the provisions of this Section 8(b)  and insuring that this Warrant (or any such replacement security) will be similarly adjusted upon any subsequent transaction analogous t