Exhibit 4.1

AMENDMENT NO. 6

to

RIGHTS AGREEMENT

between

BEACON POWER CORPORATION

and

COMPUTERSHARE TRUST COMPANY, N.A.

(fka EQUISERVE TRUST COMPANY, N.A.)

Dated as of October 7, 2011

This AMENDMENT NO. 6, dated as of October 7, 2011 to Rights Agreement, dated as of September 25, 2002, as previously amended by Amendment No. 1 dated as of December 27, 2002, Amendment No. 2 dated as of August 8, 2007, Amendment No. 3 dated as of October 24, 2007, Amendment No. 4 dated as of February 18, 2009 and Amendment No. 5 dated as of June 19, 2009 (as amended, the “Rights Agreement”), is between Beacon Power Corporation, a Delaware corporation (the “Company”), and Computershare Trust Company, N.A. (fka EquiServe Trust Company, N.A.), as Rights Agent (the “Rights Agent”).  Capitalized terms used but not defined herein have the meanings ascribed to such terms in the Rights Agreement.

WHEREAS, the Board of Directors of the Company (the “Board”) has resolved to remove the beneficial ownership exception for Seaside 88, LP; and

WHEREAS the Board has resolved to exclude from the beneficial ownership of Group Robinson LLC, a California limited liability company (“Robinson”) the shares it has a right to acquire pursuant to common stock warrant issuable under that certain Engagement Letter dated as of October 5, 2011 between Robinson and the Company;

NOW THEREFORE, in consideration of the premises and mutual agreements contained herein, the parties hereto pursuant to Section 27 of the Rights Agreement agree as follows:

1.                                       Amendments. The Rights Agreement is amended as follows:

1.1                                 Paragraph (ii) of Section 1(d) (whose preamble is “(d) A Person shall be deemed the “Beneficial Owner” of, a Person’s “Beneficial Ownership” shall include and a Person shall be deemed to “beneficially own” any securities:”) is amended and restated in its entirety to read as follows:

“(ii) which such Person or any of such Person’s Affiliates or Associates has (1) the right to acquire (whether such right is exercisable immediately or only after the passage of time) pursuant to any agreement, arrangement or understanding (other than customary agreements with and between underwriters and selling group member with respect to a bona fide public offering of securities), or upon the exercise of conversion rights, exchange rights, rights (other than these Rights), warrants or options, or otherwise; provided, however, that a Person shall not be deemed the Beneficial Owner of, or to beneficially own, (x) securities tendered pursuant to a tender or

exchange offer made by or on behalf of such Person or any of such Person’s Affiliates or Associates until such tendered securities are accepted for purchase or exchange or (y) securities which might be otherwise be acquired through exercise of a warrant but for a limitation in such warrant or elsewhere that limits exercise to those securities that would not (when added to those otherwise beneficially owned) cause the holder to become an Acquiring Person; and provided further that Group Robinson LLC shall not pursuant to either paragraph (i) or this paragraph (ii) be deemed the Beneficial Owner of, or to beneficially own, common stock of the Company that it is entitled to acquire or that is acquires pursuant to the common stock warrants issuable under that certain Engagement Letter dated as of October 5, 2011, as subsequently amended from time to time, between it and the Company; or (2) the right to vote, or the right to direct the vote, pursuant to any agreement, arrangement or understanding; provided, however, that a Person shall not be deemed the Beneficial Owner of, or to beneficially own, any security, if the agreement, arrangement or understanding to vote, or direct the vote of, such security (x) arises solely from a revocable proxy or consent given to such Person in response to a public proxy or consent solicitation made pursuant to, and in accordance with, the applicable rules and regulations promulgated under the Exchange Act and (y) is not also then reportable on Schedule 13D under the Exchange Act (or any comparable or successor report); or”

2.                                       Miscellaneous.

2.1                                 No Further Amendments. Except as specifically amended hereby, the Rights Agreement shall remain unmodified and in full force and effect, and the Rights Agreement is hereby ratified and affirmed in all respects.

2.2                                 Governing Law. This Amendment No. 6 shall be governed by and construed in accordance with the laws of the State of Delaware.

2.3                                 Counterparts. This Amendment No. 6 may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment No. 6 to be duly executed and delivered on October 7, 2011.