Exhibit 4.1

SECOND AMENDMENT TO RIGHTS AGREEMENT

THIS SECOND AMENDMENT TO RIGHTS AGREEMENT (this “Second Amendment”), dated effective as of February 13, 2012, is entered into by and between Hercules Offshore, Inc., a Delaware corporation (the “Company”), and American Stock Transfer & Trust Company LLC, as rights agent (the “Rights Agent”), pursuant to Section 27 of the Rights Agreement, dated as of October 31, 2005, as amended (the “Rights Agreement”), between the Company and the Rights Agent.

WHEREAS, Section 27 of the Rights Agreement provides that, at any time when the Rights (as defined in the Rights Agreement) are redeemable, the Company may in its sole and absolute discretion, and the Rights Agent shall, if the Company so directs, supplement or amend any provision of the Rights Agreement in any respect without the approval of any holders of Rights or holders of Common Stock (as defined in the Rights Agreement); and

WHEREAS, the Rights are currently redeemable, and the Board of Directors of the Company has determined that it is in the best interests of the Company to amend the Rights Agreement to accelerate the Final Expiration Date, as further provided herein;

NOW, THEREFORE, in consideration of the premises and mutual agreements set forth herein and in the Rights Agreement, the parties hereby agree as follows:

Section 1. Definitions. Capitalized terms used but not defined herein shall have the meaning assigned to such terms in the Rights Agreement.

Section 2. Amendment to Rights Agreement. The definition of “Final Expiration Date” shall read in its entirety as follows:

“Final Expiration Date” shall mean the close of business on February 13, 2012.”

Section 3. Miscellaneous.

(a) This Second Amendment shall be effective as of the date first above written, and, except as set forth herein, the Rights Agreement shall remain in full force and effect and shall be otherwise unaffected hereby.

(b) This Second Amendment 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.

(c) This Second Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State.

(d) Except to the extent specifically amended hereby, the provisions of the Rights Agreement shall remain unmodified, and the Rights Agreement as amended hereby is confirmed as being in full force and effect.

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IN WITNESS WHEREOF, the parties hereto have caused this Second Amendment to be duly executed and attested, all as of the day and year first above written.

[Signature Page to Second Amendment to Rights Agreement]