SECOND AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT

Exhibit 10.2

SECOND AMENDMENT TO THIRD AMENDED

AND RESTATED CREDIT AGREEMENT

This SECOND AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT (this “Second Amendment”), dated as of May 5, 2014 (the “Second Amendment Effective Date”), is among MARTIN OPERATING PARTNERSHIP L.P., a Delaware limited partnership, as borrower (the “Borrower”), MARTIN MIDSTREAM PARTNERS L.P., a Delaware limited partnership (the “MLP”), the Lenders (as defined below) party hereto, and ROYAL BANK OF CANADA, as administrative agent (the “Administrative Agent”) and collateral agent for the Lenders and as L/C Issuer and a Lender.

WHEREAS, the Borrower, the MLP, the Administrative Agent, and the lenders party thereto (the “Lenders”) are parties to that certain Third Amended and Restated Credit Agreement dated as of March 28, 2013 (as amended by that certain First Amendment to Third Amended and Restated Credit Agreement dated as of July 12, 2013, and as may be further renewed, extended, amended, restated or modified from time to time, the “Credit Agreement”);

WHEREAS, the Borrower has notified the Administrative Agent that the Borrower intends to purchase from Atlas Pipeline Mid-Continent Holdings, LLC, a Delaware limited liability company, 100% of the membership interests in Atlas Pipeline NGL Holdings, LLC, a Delaware limited liability company, and Atlas Pipeline NGL Holdings II, LLC, a Delaware limited liability company, which entities own a 20% partnership interest in West Texas LPG Pipeline Limited Partnership, a Texas limited partnership (the “West Texas LPG”), which owns an NGL transmission system, comprised of a 19.8% limited partner interest and a 0.2% general partner interest;

WHEREAS, the Borrower has requested that the Administrative Agent and Required Lenders amend the Credit Agreement in connection with the West Texas LPG investment to reflect the changes set forth below; and

WHEREAS, the Administrative Agent and Required Lenders have agreed to such request, subject to the terms and conditions set forth herein.

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

SECTION 1. Definitions. Unless otherwise defined in this Second Amendment, terms used in this Second Amendment that are defined in the Credit Agreement shall have the meanings assigned to such terms in the Credit Agreement (as amended by this Second Amendment). The interpretive provisions set forth in Section 1.02 of the Credit Agreement shall apply to this Second Amendment.

SECTION 2. Amendment to Credit Agreement. In reliance on the representations, warranties, covenants and agreements contained in this Second Amendment, but subject to the satisfaction of each condition precedent set forth in Section 3 hereof, the Credit Agreement shall be amended effective as of the Second Amendment Effective Date in the manner provided in this Section 1.

(a) Amended Definition. The definition of “Loan Document” contained in Section 1.01 of the Credit Agreement shall be amended and restated in its entirety to read in full as follows:

“Loan Documents” means this Agreement, the First Amendment, the Second Amendment, each Note, the Master Consent to Assignment, each of the Collateral

Documents, the Agent/Arranger Fee Letters, the Engagement Letter, each Committed Loan Notice, each Compliance Certificate, the Guaranties, each Letter of Credit Application and each other agreement, document or instrument executed and delivered by a Loan Party from time to time in connection with this Agreement and the Notes.

(b) New Definitions. Section 1.01 of the Credit Agreement shall be amended to add the following definitions to such Section in appropriate alphabetical to read in full as follows:

“First Amendment” means that certain First Amendment to Third Amended and Restated Credit Agreement dated as of July 12, 2013 by and among the Borrower, MLP, the other Loan Parties party thereto, the Lenders party thereto, the Administrative Agent and the Collateral Agent.

“Initial WTP Investment” means the total consideration provided (including, without limitation, any earn out obligations, purchase price adjustments or future payment obligations) for the initial investment by the Borrower or the applicable Loan Party in West Texas LPG pursuant to the WTP Documents.

“Second Amendment” means that certain Second Amendment to Third Amended and Restated Credit Agreement dated as of May 5, 2014 by and among the Borrower, MLP, the other Loan Parties party thereto, the Lenders party thereto, the Administrative Agent and the Collateral Agent.

“Second Amendment Effective Date” means May 5, 2014.

“West Texas LPG” means West Texas LPG Pipeline Limited Partnership, a Texas limited partnership.

“WTP Documents” means, collectively, (a) that certain Purchase and Sale Agreement between the Borrower and Atlas Pipeline Mid-Continent Holdings, LLC, a Delaware limited liability company, pursuant to which the Borrower has agreed to acquire, subject to the terms and conditions set forth therein, 100% of the membership interests in Atlas Pipeline NGL Holdings, LLC, a Delaware limited liability company, and Atlas Pipeline NGL Holdings II, LLC, a Delaware limited liability company, which entities own a 19.8% limited partner interest and a 0.2% general partner interest in West Texas LPG and (b) the WTP Limited Partnership Agreement.

“WTP Limited Partnership Agreement” means the First Amended and Restated Limited Partnership Agreement of West Texas LPG, dated as of May 1, 1999, as amended by that Amendment to First Amended and Restated Limited Partnership Agreement of the West Texas LPG Pipeline Limited Partnership dated February 2, 2004, but effective August 8, 2003.

(c) Amendment to Section 7.02(a)(viii)(C) of the Credit Agreement. Section 7.02(a)(viii)(C) of the Credit Agreement shall be amended and restated in its entirety to read in full as follows:

(C) the aggregate outstanding amount of Investments made after the Closing Date in Permitted Joint Ventures (other than Cardinal and West Texas LPG) shall not exceed $50,000,000 (as such amount may be increased on a dollar-for-dollar basis by Returned Capital with respect to any such Investment); provided that, with respect to the

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Initial WTP Investment, (1) the Borrower or the applicable Loan Party shall have consummated the Initial WTP Investment on or prior to December 31, 2014 in accordance with all applicable Laws and the terms of the WTP Documents, with all of the material conditions precedent thereto having been satisfied in all material respects by the parties thereto, and such terms being substantially the same as those set forth in the WTP Documents provided to the Administrative Agent as of the Second Amendment Effective Date unless the Administrative Agent has approved the amendment, waiver, supplement or modification thereof (such approval not to be unreasonably withheld or delayed), (2) the amount of the Initial WTP Investment shall not exceed $140,000,000, and (3) the Borrower or the applicable Loan Party shall have pledged its equity interests in West Texas LPG to the Collateral Agent in accordance with Section 6.16; and

(d) Amendment to Section 7.13 of the Credit Agreement. Section 7.13 of the Credit Agreement shall be amended by inserting the following phrase immediately before the period at the end of Section 7.13 of the Credit Agreement to read in full as follows:

, or any amendment, modification, waiver or supplement to the WTP Documents that alters the voting provisions in the WTP Limited Partnership Agreement to require the approval of less than two general partners of West Texas LPG or otherwise materially and adversely affect the voting rights of any Loan Party under the WTP Limited Partnership Agreement.

(e) Amendment to Section 7.15 of the Credit Agreement. Clause (x) of the proviso at the end of Section 7.15 of the Credit Agreement shall be amended by replacing the reference to “Cardinal or MET” therein with a reference to “Cardinal, MET or West Texas LPG”; and

SECTION 3. Conditions of Effectiveness. This Second Amendment shall not be effective until the date each of the following conditions precedent has been satisfied:

(a) the Administrative Agent has received a counterpart of this Second Amendment executed by the Borrower, the MLP, the other Loan Parties, the Administrative Agent, and Required Lenders (which may be by telecopy or other electronic transmission);

(b) the Borrower shall have paid to the Administrative Agent an amendment fee for the account of each Lender party hereto in an amount for each such Lender equal to 5.0 bps (0.05%) of the amount of such Lender’s Committed Sum in effect on the Second Amendment Effective Date and other fees and expenses due and payable on the date hereof;

(c) the Administrative Agent shall have received substantially final versions, certified as true and complete by a Responsible Officer of the Borrower, of each of the WTP Documents, which documents shall have terms and conditions reasonably satisfactory to the Administrative Agent; and

(d) the Administrative Agent has received such other documents as may be reasonably required by the Administrative Agent.

SECTION 4. Representations and Warranties. In order to induce the Administrative Agent and the Required Lenders to enter into this Second Amendment, each Loan Party represents and warrants to the Administrative Agent and to each Lender that:

(a) This Second Amendment, the Credit Agreement as amended hereby, and each Loan Document have been duly authorized, executed, and delivered by the Borrower and the applicable Loan

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Parties and constitute their legal, valid, and binding obligations enforceable in accordance with their respective terms (subject, as to the enforcement of remedies, to applicable bankruptcy, reorganization, insolvency, moratorium, and similar laws affecting creditors’ rights generally and to general principles of equity).

(b) The representations and warranties set forth in Article V of the Credit Agreement and in the Collateral Documents are true and correct in all material respects on and as of the Second Amendment Effective Date, after giving effect to this Second Amendment, as if made on and as of the Second Amendment Effective Date, except to the extent such representations and warranties relate solely to an earlier date.

(c) As of the date hereof, after giving effect to this Second Amendment, no Default or Event of Default has occurred and is continuing or would result immediately after giving effect to this Second Amendment and the transactions contemplated hereby.

(d) No Loan Party has any defense to payment, counterclaim or rights of set-off with respect to the Obligations on the date hereof.

SECTION 5. Effect of Amendment.

(a) This Second Amendment (i) except as expressly provided herein, shall not be deemed to be a consent to the modification or waiver of any other term or condition of the Credit Agreement or of any of the instruments or agreements referred to therein, and (ii) shall not prejudice any right or rights which the Administrative Agent, the Collateral Agent, or the Lenders may now or hereafter have under or in connection with the Credit Agreement, as amended by this Second Amendment. Except as otherwise expressly provided by this Second Amendment, all of the terms, conditions and provisions of the Credit Agreement shall remain the same. It is declared and agreed by each of the parties hereto that the Credit Agreement, as amended hereby, shall continue in full force and effect, and that this Second Amendment and such Credit Agreement shall be read and construed as one instrument.

(b) Each of the undersigned Guarantors is executing this Second Amendment in order to evidence that it hereby consents to and accepts the terms and conditions of this Second Amendment and the transactions contemplated thereby, agrees to be bound by the terms and conditions hereof, and ratifies and confirms that each Guaranty and each of the other Loan Documents to which it is a party is, and shall remain, in full force and effect after giving effect to this Second Amendment. The Borrower and each of the other Loan Parties hereby confirm and agree that all Liens and other security now or hereafter held by the Collateral Agent for the benefit of the Lenders as security for payment of the Obligations are the legal, valid, and binding obligations of the Borrower and the Loan Parties, remain in full force and effect, are unimpaired by this Second Amendment, and are hereby ratified and confirmed as security for payment of the Obligations.

(c) No failure or delay on the part of the Administrative Agent or the Lenders to exercise any right or remedy under the Credit Agreement, any other Loan Document or applicable law shall operate as a waiver thereof, nor shall any single partial exercise of any right or remedy preclude any other or further exercise of any right or remedy, all of which are cumulative and may be exercised without notice except to the extent notice is expressly required (and has not been waived) under the Credit Agreement, the other Loan Documents and applicable law.

SECTION 6. Miscellaneous. This Second Amendment shall for all purposes be construed in accordance with and governed by the laws of the State of New York and applicable federal law. The captions in this Second Amendment are for convenience of reference only and shall not define or limit the

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provisions hereof. This Second Amendment may be executed in separate counterparts, each of which when so executed and delivered shall be an original, but all of which together shall constitute one instrument. In proving this Second Amendment, it shall not be necessary to produce or account for more than one such counterpart. Delivery of an executed counterpart of this Second Amendment by telecopier or other electronic means shall be effective as delivery of a manually executed counterpart of this Second Amendment.

SECTION 7. Entire Agreement. THE CREDIT AGREEMENT (AS AMENDED BY THIS SECOND AMENDMENT) AND THE OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

Remainder of Page Intentionally Blank.

Signature Pages to Follow.

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IN WITNESS WHEREOF, the parties hereto have caused this Second Amendment to be duly executed and delivered by their proper and duly authorized officers as of the date and year first above written.

[SIGNATURE PAGE TO THE SECOND AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT – MARTIN OPERATING PARTNERSHIP L.P.]

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