BEACON POWER CORPORATION WARRANT AMENDMENT AND EXERCISE AGREEMENT

Exhibit 10.4

BEACON POWER CORPORATION

WARRANT AMENDMENT AND EXERCISE AGREEMENT

This Agreement (the “Agreement”) dated May 31, 2011 relates to Warrant Number U-2 dated October 15, 2008 (the “Warrant”) issued by Beacon Power Corporation, a Delaware corporation (the “Company”) to Alpha Capital AG (the “Holder”), pursuant to which the Holder is entitled to subscribe for and purchase up to 870,000 shares of the voting common stock of the Company, par value $0.01 per share (the “Common Stock”). Capitalized terms used but not defined in this Agreement have the meanings given to them in the Warrant.

WHEREAS, the Company wishes to amend the Warrant, and the Holder wishes to exercise the Warrant in part according to its terms;

NOW, THEREFORE, for good and valuable consideration, the parties hereto agree as follows:

1.                                       Amendments.

1.1                                 The definition of “Exercise Price” in Section 1(b) of the Warrant is hereby amended and restated in its entirety as follows:

“(b)  Exercise Price.  For purposes of this Warrant, “Exercise Price” means $1.40, subject to adjustment as provided herein.”

1.2                                 The definition of “Expiration Date” in Section 15(j) of the Warrant is hereby amended and restated in its entirety as follows:

“(j)  “Expiration Date” means November 1, 2011.”

1.3                                 All other terms of the Warrant shall remain unchanged.

2.                                       In consideration of the execution by the Company of this Agreement, the Holder agrees to exercise the Warrant in part for 435,000 shares of Common Stock (the “Partial Exercise”) on the date hereof.

3.                                       Upon execution and delivery of the related exercise notice, the Company shall, in accordance with the terms of the Warrant, issue a replacement warrant to the Holder representing the right to purchase the remaining number of Warrant Shares at the amended Exercise Price, in accordance with Section 7 of the Warrant.

4.                                       The Company represents, warrants and agrees that:

4.1                                 it has all the requisite authority and power to enter into and consummate the transactions contemplated herein and such transactions shall not contravene any contractual, regulatory, statutory or other obligation or restriction applicable to the Company;

4.2                                 this Agreement has been duly and validly authorized, executed and delivered by the Company, and shall constitute a legal, valid, and binding obligation of the Company, enforceable against it in accordance with its terms, except as the enforcement thereof may be limited by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium, or similar laws affecting the enforcement of creditors’ rights generally and general equitable principles whether in a proceeding in equity or at law;

4.3                                 it has a sufficient number of authorized and unissued shares of voting common stock to issue upon the exericse of the Warrant;

4.4                                 any shares issued to Holder pursuant to the Partial Exercise of the Warrant shall be registered under the Company’s effective shelf registration statement on Form S-3 (File No. 333-152140) and shall be freely tradable, subject to the accuracy of Holder’s representations in Section 5.4 below;

4.5                                 it shall, by 9:00 a.m. (New York City time) on June 1, 2011 file a Current Report on Form 8-K disclosing the material terms of the transactions contemplated hereby. From and after the filing of such report, the Company represents to the Holder that it shall have publicly disclosed all material, non-public information delivered to the Holder by the Company; and

4.6                                 it is not entering into any other financing transaction concurrently with this Agreement.

5.                                       The Holder represents and warrants that:

5.1                                 it has the authority to enter into the transactions and consummate the transactions contemplated herein and such transactions shall not contravene any contractual, regulatory, statutory or other obligation or restriction applicable to the Holder;

5.2                                 this Agreement has been duly and validly authorized, executed and delivered by the Holder, and shall constitute a legal, valid, and binding obligation of the Holder, enforceable against it in accordance with its terms, except as the enforcement thereof may be limited by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium, or similar laws affecting the enforcement of creditors’ rights generally and general equitable principles whether in a proceeding in equity or at law;

5.3                                 it has sufficient knowledge and experience in financial and business matters so as to be capable of bearing the economic risks of participation in this Agreement, and it is capable of evaluating the merits and risks of participating in this Agreement, including any risks associated with surrendering certain rights related to the Warrants; and

5.4                                 it is not an affiliate of the Company as such term is defined in Rule 144 promulgated under the Act.

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6.                                       Miscellaneous. This Agreement may be executed in multiple original counterparts, each of which shall be an original, but all of which shall constitute one and the same Agreement.  This Agreement and all rights, obligations and liabilities hereunder shall be governed by, and construed in accordance with, the internal laws of the State of New York, without giving effect to the principles of conflicts of law that would require the application of the laws of any other jurisdiction.

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IN WITNESS WHEREOF, the Holder and the Company have executed this Agreement as of May 31, 2011.

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