CLASS C COMMON STOCK AND NOTE PURCHASE AGREEMENT

Exhibit 10.31

EXECUTION COPY

LUNA INNOVATIONS INCORPORATED

CLASS C COMMON STOCK AND NOTE PURCHASE AGREEMENT

December 30, 2005

TABLE OF CONTENTS

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TABLE OF CONTENTS

(continued)

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EXHIBITS

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LUNA INNOVATIONS INCORPORATED

CLASS C COMMON STOCK AND NOTE PURCHASE AGREEMENT

This Class C Common Stock and Note Purchase Agreement (this “ Agreement ”) is made as of December 30, 2005, by and between Luna Innovations Incorporated, a Delaware corporation (the “ Company ”), and Carilion Health System, a Virginia non-profit, non-stock corporation (the “ Investor ”).

WHEREAS , the Company and the Investor are parties to that certain Class C Common Stock Purchase Agreement dated as of August 2, 2005 (the “ Prior Agreement ”), pursuant to which the Investor purchased, and the Company sold and issued to the Investor, 2,639,688 shares (the “ Original Class C Shares ”) of the Company’s Class C Common Stock, par value $0.001 per share (the “ Class C Common Stock ”) at the First Closing (as defined in the Prior Agreement);

WHEREAS , the Prior Agreement contemplated the sale and issuance of (i) an additional 1,885,491 shares of Class C Common Stock (the “ Second Tranche Shares ”), subject to the satisfaction of certain conditions precedent, at a Second Closing (as defined in the Prior Agreement) and (ii) an additional 1,131,294 shares of Class C Common Stock (the “ Third Tranche Shares ”), subject to the satisfaction of certain conditions precedent, at a Third Closing (as defined in the Prior Agreement);

WHEREAS , the Company and the Investor have determined, among other things, that (i) the sale and issuance of the Second Tranche Shares at a Second Closing (as defined in the Prior Agreement) shall not occur and (ii) the sale and issuance of the Third Tranche Shares at a Third Closing (as defined in the Prior Agreement) shall occur on modified terms as set forth in this Agreement;

WHEREAS , the Company and the Investor desire to terminate the Prior Agreement and enter into this Agreement;

WHEREAS , the Company and the Investor are parties to that certain Investor Rights Agreement dated as of August 2, 2005 (the “ Prior Investor Rights Agreement ”) and that certain Right of First Refusal, Co-Sale and Voting Agreement dated as of August 2, 2005 (the “ Right of First Refusal, Co-Sale and Voting Agreement ”); and

WHEREAS , the Company and the Investor desire that (i) the Prior Investor Rights Agreement be amended and restated as of the date hereof to reflect certain changes and (ii) the Right of First Refusal, Co-Sale and Voting Agreement survive Closing (as defined below) without modification or amendment.

NOW, THEREFORE , in consideration of the foregoing and the representations, warranties and conditions set forth below, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged and agreed, the parties hereto, intending to be legally bound, hereby agree as follows:

SECTION 1

Authorization, Sale and Issuance of the Notes and the Class C Common Stock.

1.1 Authorization . The Company will, prior to the Closing (as defined below), authorize the sale and issuance, pursuant to the terms of this Agreement, of five (5) convertible promissory notes, each in the principal amount of one million dollars ($1,000,00.00), and each in substantially the form attached hereto as Exhibit A (each a “ Note ” and collectively the “ Notes ”) and 1,131,294 shares (the “ Class C Shares ”) of the Company’s Class C Common Stock, par value $0.001 per share (the “ Class C Common Stock ”), having the rights, privileges, preferences and restrictions set forth in the Amended and Restated Certificate of Incorporation of the Company, in substantially the form attached hereto as Exhibit B (the “ Restated Certificate ”). The Company will, prior to the Closing (as defined below), authorize and reserve: (i) 1,885,490 shares of Class C Common Stock for issuance upon conversion of the principal amount of the Notes prior to the Company’s IPO (as defined in the Notes) in accordance with their terms (the “ Class C Note Conversion Shares ”); (ii) 905,035 shares of Class B Common Stock, par value $0.001 per share (the “ Class B Common Stock ”) for issuance upon conversion of the maximum amount of accrued interest under the Notes prior to the Company’s IPO in accordance with their terms (the “ Class B Note Conversion Shares ”); (iii) 2,790,525 shares of Common Stock, par value $0.001 per share (the “ Common Stock ”) for issuance upon conversion of the principal and maximum amount of accrued interest under the Notes on or after the date of the Company’s IPO in accordance with their terms (the “ Common Note Conversion Shares ” and together with the Class C Note Conversion Shares and the Class B Note Conversion Shares, the “ Note Conversion Shares ”); (iv) 1,131,294 shares of Class C Common Stock for sale and issuance of the Class C Shares under this Agreement; (v) 2,149,145 shares of Class A Common Stock, par value $0.001 per share (the “ Class A Common Stock ”) and 3,507,327 shares of Class B Common Stock for issuance upon conversion of the Class C Shares, the Class C Note Conversion Shares and the Original Class C Shares (such shares of Class A Common Stock and Class B Common Stock collectively, the “ Conversion Shares ”) and (vi) 5,656,472 shares of Common Stock for issuance upon the conversion of the Class B Note Conversion Shares and the conversion of the Conversion Shares.

1.2 Sale and Issuance of Notes and Class C Shares . Subject to the terms and conditions of this Agreement, the Investor agrees to purchase, and the Company agrees to sell and issue to the Investor, (i) the Notes in the principal amounts set forth on Exhibit C attached hereto (the “ Note Purchase Prices ”) and (ii) the number of Class C Shares for the aggregate purchase price set forth on Exhibit C attached hereto (the “ Class C Shares Purchase Price ” and together with the Note Purchase Prices the “ Aggregate Purchase Price ”).

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SECTION 2

Closing Date and Delivery of the Notes and the Class C Common Stock.

2.1 Closing . The purchase, sale and issuance of the Notes and the Class C Shares shall take place at a closing (the “ Closing ”) at the offices of Woods Rogers PLC, 10 South Jefferson Street, Suite 1400, Roanoke, Virginia 24011, at 10:00 a.m. local time on the date of this Agreement or such other date and time as the Company and the Investor mutually agree.

2.2 Delivery . At the Closing, the Company will deliver to the Investor (i) the Notes to be purchased by such Investor and (ii) a certificate registered in such Investor’s name representing the number of Class C Shares that such Investor is purchasing in such Closing, against payment of the Aggregate Purchase Price therefor as set forth on Exhibit C , by (a) check payable to the Company, (b) wire transfer in accordance with the Company’s instructions, (c) cancellation of indebtedness or (d) any combination of the foregoing. In the event that payment by the Investor is made, in whole or in part, by cancellation of indebtedness, then such Investor shall surrender to the Company for cancellation at the Closing any evidence of indebtedness or shall execute an instrument of cancellation in form and substance acceptable to the Company.

2.3 Termination of Prior Agreement . Effective upon the Closing, the Prior Agreement (except for the representations and warranties of the Company and Investor contained in Sections 3 and 4, respectively, which shall survive until August 4, 2007) is hereby terminated and of no further force or effect. For purposes of clarity, the Prior Investor Rights Agreement shall be amended and restated as of the date hereof and the Right of First Refusal, Co-Sale and Voting Agreement shall survive the Closing without modification or amendment.

SECTION 3

Representations and Warranties of the Company.

A Schedule of Exceptions is attached hereto as Exhibit D (the “ Schedule of Exceptions ”). Except as set forth on the Schedule of Exceptions, the Company hereby represents and warrants to the Investor, effective as of each Closing (unless otherwise set forth herein), as follows:

3.1 Organization, Good Standing and Qualification . The Company is a corporation duly organized, validly existing and in good standing under the laws of the State of Delaware. The Company has the requisite corporate power and authority to own and operate its properties and assets, to carry on its business as presently conducted, to execute and deliver this Agreement and the Notes (collectively, together with the exhibits and schedule hereto and thereto, the “ Agreements ”), to issue and sell the Notes, the Class C Shares, the Note Conversion Shares and the Conversion Shares and to perform its obligations pursuant to the Agreements, the Company’s Amended and Restated Bylaws (the “ Bylaws ”) and the Restated Certificate. The Company is presently qualified to do business as a foreign corporation in each jurisdiction where the failure to be so qualified would have a material adverse effect on the Company’s financial condition or business as presently conducted (a “ Material Adverse Effect ”).

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3.2 Subsidiaries . The Company does not own or control, directly or indirectly, any interest in any corporation, partnership, limited liability company, association or other business entity, except as set forth on the Schedule of Exceptions.

3.3 Capitalization .

(a) Immediately prior to the Closing, the authorized capital stock of the Company will consist of 7,164,463 shares of Class A Common Stock (of which 5,015,318 shares are issued and outstanding), 13,707,297 shares of Class B Common Stock, (of which 1,732,477 shares are issued and outstanding), 5,656,472 shares of Class C Common Stock (of which 2,639,688 shares are issued and outstanding), and 23,257,094 shares of Common Stock (none of which are issued and outstanding). The Class A Common Stock, Class B Common Stock, Class C Common Stock and Common Stock shall have the rights, preferences, privileges and restrictions set forth in the Restated Certificate.

(b) The outstanding shares have been duly authorized and validly issued in compliance with applicable laws, and are fully paid and nonassessable.

(c) The Company has reserved as of the Closing:

(i) 1,131,294 shares of Class C Common Stock for issuance at Closing pursuant to this Agreement;

(ii) 1,885,490 shares of Class C Common Stock for issuance upon conversion of the principal amount of the Notes prior to the Company’s IPO (as defined in the Notes) in accordance with their terms;

(iii) 905,035 shares of Class B Common Stock for issuance upon conversion of the maximum amount of accrued interest under the Notes prior to the Company’s IPO in accordance with their terms;

(iv) 2,790,525 shares of Common Stock for issuance upon conversion of the principal and maximum amount of accrued interest under the Notes on or after the date of the Company’s IPO in accordance with their terms;

(v) 2,149,145 shares of Class A Common Stock and 3,507,327 shares of Class B Common Stock for issuance upon conversion of the Class C Shares, the Class C Note Conversion Shares and the Original Class C Shares;

(vi) 5,656,472 shares of Common Stock for issuance upon the conversion of the Class B Note Conversion Shares and the conversion of the Conversion Shares; and

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(vii) 8,000,000 shares of Class B Common Stock authorized for issuance to employees, consultants and directors pursuant to the Company’s 2003 Stock Plan (the “ Stock Plan ”), of which options to purchase 7,154,084 shares of Class B Common Stock are issued and outstanding as of the date of this Agreement and options to purchase 518,123 shares of Class B Common Stock have previously been exercised.

(d) The outstanding shares of Class A Common Stock, Class B Common Stock, Class C Common Stock and Common Stock are owned by the stockholders and in the numbers specified in Exhibit E attached hereto.

(e) All options granted and outstanding vest as follows: twenty-five percent (25%) of the shares vest one (1) year following the vesting commencement date, with the remaining seventy-five percent (75%) vesting in equal monthly installments over the next three (3) years. No stock plan, stock purchase, stock option or other agreement or understanding between the Company and any holder of any equity securities or rights to purchase equity securities provides for acceleration or other changes in the vesting provisions or other terms of such agreement or understanding as the result of (i) termination of employment (whether actual or constructive); (ii) any merger, consolidated sale of stock or assets, change in control or any other transaction(s) by the Company; or (iii) the occurrence of any other event or combination of events.

(f) The Class C Shares, when issued and delivered and paid for in compliance with the provisions of this Agreement, will be validly issued, fully paid and nonassessable. The Conversion Shares have been duly and validly reserved and, when issued in compliance with the provisions of this Agreement, the Restated Certificate and applicable law, will be validly issued, fully paid and nonassessable. The Class C Shares and the Conversion Shares will be free of any liens or encumbrances, other than any liens or encumbrances created by or imposed upon the Investor; provided , however , that the Class C Shares and the Conversion Shares are subject to restrictions on transfer under U.S. state and/or federal securities laws and as set forth herein and in that Amended and Restated Investor Rights Agreement by and among the Company, the Investor and certain stockholders of the Company of even date herewith in substantially the form attached hereto as Exhibit F (the “ Investor Rights Agreement ”). Except as set forth in the Right of First Refusal, Co-Sale and Voting Agreement by and among the Company and certain of the Company’s stockholders dated August 2, 3005 (the “ ROFR, Co-Sale and Voting Agreement ”), the Class C Shares and the Conversion Shares are not subject to any preemptive rights or rights of first refusal.

(g) Except for the rights provided pursuant to the Investor Rights Agreement and the ROFR, Co-Sale and Voting Agreement, or as otherwise described in this Agreement, there are no options, warrants or other rights to purchase any of the Company’s authorized and unissued capital stock.

3.4 Authorization . All corporate action on the part of the Company and its directors, officers and stockholders necessary for the authorization, execution and delivery of the Agreements by the Company, the authorization, sale, issuance and delivery of the Notes, the Class C Shares, the Note Conversion Shares and the Conversion Shares, and the performance of all of the Company’s obligations under the Agreements, the Restated Certificate and Bylaws has been taken or will be

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taken prior to the Closing. The Agreements, when executed and delivered by the Company, shall constitute valid and binding obligations of the Company, enforceable in accordance with their terms, except (i) as limited by laws of general application relating to bankruptcy, insolvency and the relief of debtors, (ii) as limited by rules of law governing specific performance, injunctive relief or other equitable remedies and by general principles of equity, and (iii) to the extent the indemnification provisions contained in the Agreements may further be limited by applicable laws and principles of public policy.

3.5 Financial Statements . The Company has delivered to the Investor the unaudited balance sheet and statement of operations of the Company as of and for the 12-month period ended December 31, 2004 and unaudited balance sheet and statement of operations of the Company as of the nine-month period ended September 30, 2005 (the “ Financial Statements ”). The Financial Statements have been prepared in accordance with the books and records of the Company, have been prepared in accordance with accounting principles generally accepted in the United States (“ GAAP ”) applied on a consistent basis throughout the periods indicated and are correct in all material respects and present fairly the financial condition and operating results of the Company as of the date(s) and during the period(s) indicated therein. Except as disclosed in the Financial Statements, the Company is not a guarantor or indemnitor of any indebtedness of any other person. The Company maintains and will continue to maintain a standard system of accounting established and administered in a manner to produce financial reports in accordance with GAAP.

3.6 Changes . Since September 30, 2005, there has not been:

(a) any change in the assets, liabilities, financial condition or operating results of the Company from that reflected in the Financial Statements, except changes in the ordinary course of business, that has had a Material Adverse Effect;

(b) any damage, destruction or loss, whether or not covered by insurance, that has had a Material Adverse Effect;

(c) any change or amendment to an agreement by which the Company or any of its assets or properties is bound or subject that has had a Material Adverse Effect;

(d) any resignation or termination of any executive officer or key employee of the Company;

(e) any sale, assignment or transfer of any patents, trademarks, copyrights, trade secrets or other material intangible assets; or

(f) any mortgage, pledge, transfer of a security interest in, or lien, created by the Company, with respect to any of its material properties or assets, except liens for taxes not yet due or payable.

3.7 Material Contracts . Except for the agreements explicitly contemplated hereby, there are no agreements, understandings, instruments, contracts, proposed transactions, judgments, orders,

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writs or decrees to which the Company is a party or by which it is bound which may involve (i) obligations of, or payments to, the Company in excess of $50,000 (other than obligations of, or payments to, the Company arising from purchase or sale agreements entered into in the ordinary course of business), (ii) the license of any patent, copyright, trade secret or other proprietary right to or from the Company, or (iii) the grant of rights to manufacture, produce, assemble, license, market or sell the Company’s products or affect the Company’s exclusive right to develop, manufacture, assemble, distribute, market or sell its products (each, a “ Material Contract ”, collectively the “ Material Contracts ”). All of the Material Contracts are valid, binding and in full force and effect in all material respects, subject to laws of general application relating to bankruptcy, insolvency and the relief of debtors and rules of law governing specific performance, injunctive relief or other equitable remedies and to general principles of