Exhibit 3.1

SECOND AMENDMENT TO

SECOND AMENDED AND RESTATED OPERATING AGREEMENT

OF BLACK ELK ENERGY OFFSHORE OPERATIONS, LLC

This Second Amendment (the “Amendment”) to the Second Amended and Restated Limited Liability Company Operating Agreement, of BLACK ELK ENERGY OFFSHORE OPERATIONS, LLC, a Texas limited liability company (the “Company”), is made and entered into as of the 31st day of May, 2011.

BACKGROUND

A. The Company and its Members entered into a Second Amendment and Restated Operating Agreement, dated as of July 13, 2009, and a First Amendment thereto on August 19, 2010 (the “Operating Agreement”).

B. The Company desires to make certain amendments to the Operating Agreement.

C. Pursuant to, and in accordance with, Section 17.2 of the Operating Agreement, the Board, including the affirmative vote of the Platinum Manager, and holders of a majority of the Class B Units have consented to the amendment as set forth herein.

D. Pursuant to, and in accordance with Section 5.4(b) of the Operating Agreement, Platinum has consented to the issuance of the Units as set forth in this Amendment.

E. The Company desires to establish a new preferred class of membership units Class D Preferred Units for distribution.

F. The Company desires to revise Exhibit C to the Operating Agreement to reflect the above referenced issuances.

NOW, THEREFORE, with the foregoing Background deemed incorporated by reference herein and for good and valuable consideration, the receipt and sufficiency of which hereby are acknowledged, the parties hereby agree as follows:

1. All capitalized terms used herein and not otherwise defined herein shall have the meaning ascribed to such terms in the Operating Agreement.

2. The following definitions in Section 1.1 of the Operating Agreement are hereby amended and restated as follows:

“Sharing Ratio” means, with respect to each Member and any Person that acquires all or any portion of the Units initially issued to and held by such Member, the percentage derived by dividing (i) the number of Units held by such Member by (ii) the number of all Units held by all Members (and such percentage shall be allocated among such original Member and any such acquiring Person or Persons according to the transfer documentation pursuant to which all or any portion of such Units are Transferred from

time to time). For the avoidance of doubt, the Sharing Ratio of a Class A Member, Class B Member, Class C Member, or other class of member shall be determined (for example, for purposes of Section 11.1(c)(iv)), by taking into account under clause (i) of the preceding sentence only the Class A Units, Class B Units, Class C Units, or other class of Units held by such Member. Notwithstanding the preceding provisions of this definition, Class D Preferred Units shall be treated as not being issued for purposes of determining Sharing Ratios (i.e., they are not added to the denominator described in clause (ii) above).

“Unit” shall mean, any Class A Unit, any Class B Unit, any Class C Unit, any Class D Preferred Unit or any other class of Units as may be created and issued by the Board from time to time, issued to any Member pursuant to this Agreement, representing, subject to the terms of any such Unit, such Member’s ownership interest and rights as a Member in the Company as set forth in this Agreement, including the Member’s right to a share of the Net Profit and Net Loss of the Company, its right to Distributions and to a share of the assets of the Company on liquidation.

“Voting Units” shall mean, collectively, the Class A Units, the Class B Units, and any other class of Units that entitle the holders thereof to vote with respect to a particular matter related to the Company, but only with respect to and to the extent of such entitlement. The Class C Units and the Class D Preferred Units are not Voting Units.

3. The following definitions in Section 1.1 of the Operating Agreement are hereby added:

“Class D Member” shall mean any Member that holds Class D Preferred Units, in such Member’s capacity as a holder of such Class D Preferred Units as set forth on Exhibit C hereto, which may be amended from time to time as set forth herein.

“Class D Preferred Liquidation Value” means, with respect to any Class D Preferred Unit, the amount, as of any date of determination, which is distributable with respect to such Class D Preferred Unit pursuant to Sections 11.1(c)(i) and (ii).

“Class D Preferred Return” means, with respect to any Class D Preferred Unit, an amount equal to a twenty four percent per annum return on the Unreturned Class D Capital balance attributable to such Class D Preferred Unit, compounded annually to the extent not distributed annually.

“Class D Preferred Unit” shall mean a Unit having the rights and obligations specified with respect to Class D Preferred Units in this Agreement.

“Unreturned Class D Capital” means, with respect to each Class D Preferred Unit, an amount equal to the Capital Contribution contributed in exchange for the issuance of such Class D Preferred Unit (equal to Thirty Million Dollars ($30,000,000) for all the Class D Preferred Units), reduced by distributions with respect to such Class D Preferred Unit pursuant to Section 11.1(c)(ii), including Tax Distributions, if any, which offset such distributions.

4. Section 5.4(a) of the Operating Agreement is hereby amended and restated as follows:

“Each Class A Unit and each Class B Unit shall carry the right to one (1) vote at any meeting of the Members. The Board may, upon the request and approval of any Member, designate such Member’s Units as nonvoting. Class C Units and Class D Preferred Units do not carry the right to vote.”

5. Section 8.1(b) of the Operating Agreement is hereby amended and restated as follows:

“The issued and outstanding Units consist of Class A Units, Class B Units, Class C Units and Class D Preferred Units. The number of Units held by each Member is set out on Exhibit C opposite such Member’s name.”

6. Section 8.3 of the Operating Agreement is hereby added as follows:

“8.3 Class D Preferred Units. The powers, preferences, rights, restrictions, and other matters relating to the Class D Preferred Units are as follows:

(a) Class D Preferred Return. The holders of the Class D Preferred Units shall be entitled to receive the Class D Preferred Return pursuant to the provisions of this Agreement, including, without limitation, Sections 8.3, 11.2, and 15.2.

(b) Redemption by the Company. The Company may redeem, at any time and from time to time, without penalty, all or a portion of the outstanding Class D Preferred Units at a price per Unit in cash equal to the Class D Preferred Liquidation Value (the “Redemption Price”). The Company shall give all of the holders of the Class D Preferred Units a written notice at the last address of each holder designated on the records of the Company of its determination to effect a redemption (the “Company Redemption Notice”), specifying the redemption date (“Redemption Date”), which shall be no less than ten (10) and not more twenty (20) days after delivery of the Redemption Notice, the number of Class D Preferred Units to be redeemed, which to the extent is less than all outstanding Class D Preferred Units shall be on a pro rata basis among all holders of Class D Preferred Units in accordance with the number of Class D Preferred Units hold by such holder, and the Redemption Price. On the Redemption Date and upon receipt by the Company of evidence satisfactory to the Company of the ownership of the Class D Preferred Units, the holder thereof shall be entitled to receive payment therefor. After the Redemption Date, the Class D Preferred Units subject to a Company Redemption Notice shall no longer constitute issued and outstanding Units of the Company and shall only constitute the rights to receive Redemption Price as set forth herein

(c) Redemption by the Holder. At any time following the repayment in full of the Company’s 13.75% Senior Secure Notes due 2015, each holder of Class D Preferred Units shall have the right to cause the Company to redeem any and all of its Class D Preferred Units at the Redemption Price. Each such holder of Class D Preferred Units shall give the Company a written notice at its principal office of its desire for the Company to redeem such holder’s Class D Preferred Units (the “Holder Redemption Notice”), specifying the Redemption Date, which shall

be no less than ten (10) and not more twenty (20) days after delivery of the Holder Redemption Notice, the number of Class D Preferred Units to be redeemed and the Redemption Price. On the Redemption Date and upon receipt by the Company of evidence satisfactory to the Company of the ownership of the Class D Preferred Units, the holders thereof shall be entitled to receive payment therefor. After the Redemption Date, the Class D Preferred Units subject to the Holder Redemption Notice shall no longer constitute issued and outstanding Units of the Company and shall only constitute the rights to receive Redemption Price as set forth herein

(d) Voting Rights. Except as otherwise required by law or pursuant to Section 8.3(e) herein, each holder of Class D Preferred Units shall not be entitled to vote such Units.

7. Section 11.1(b) of the Operating Agreement is hereby amended by adding the following sentence at the end thereof:

“This Section 11.1(b) shall be applied to each class of Units separately, so that a Tax Distribution made with respect to a Class A Unit, Class B Unit, Class C Unit, or Class D Unit shall be applied to offset subsequent distributions under Section 11.1(c) only with respect to a Class A Unit, Class B Unit, Class C Unit, or Class D Unit, respectively.”

8. Section 11.1(c) of the Operating Agreement is hereby amended and restated in its entirety as follows:

“Subject to the provisions of Section 11.1 above, the Company shall make Distributions to the Members, including Distributions in kind pursuant to Section 11.2, in the order and manner set forth in this Section 11.1(c).

9. All references in the Operating Agreement to Sections 11.1(c)(i) and 11.1(c)(ii) shall be amended to refer to Sections 11.1(c)(iii) and Section 11.1(c)(iv).

10. Exhibit C of the Operating Agreement is hereby amended and restated in its entirety in accordance with the Revised Exhibit C attached hereto.

11. The Company hereby covenants and agrees that in exchange for a Capital Contribution of Thirty Million Dollars ($30,000,000), it (i) hereby issues thirty million (30,000,000) Class D Preferred Units to PPVA Black Elk (Equity) LLC.

12. Except as modified by this Amendment, the Operating Agreement shall continue unmodified and in full force and effect.

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IN WITNESS WHEREOF, pursuant to, and in accordance with, the authority granted by Section 17.2 of the Operating Agreement, and at the direction of the Board, including the Platinum Manager, the undersigned on behalf of the Company has executed this Amendment the day and year first above written.

Exhibit C

OWNERSHIP OF UNITS