Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors
Martin Midstream GP LLC:

We consent to the incorporation by reference in the registration statement (No. 333-117023) on Form S-3 of Martin Midstream Partners L.P. of our report dated March 16, 2005, with respect to the consolidated balance sheets, of Martin Midstream Partners L.P. and subsidiaries as of December 31, 2004 and 2003, and the related consolidated and combined, respectively, statements of operations, capital/equity, and cash flows of Martin Midstream Partners L.P. and subsidiaries (successor) for the years ended December 31, 2004 and 2003 and for the period from November 6, 2002 through December 31, 2002 and of Martin Midstream Partners Predecessor (predecessor) (collectively Martin Midstream) for the period from January 1, 2002 through November 5, 2002, which report appears in the December 31, 2004, annual report on Form 10-K of Martin Midstream Partners L.P. Our report refers to a change in the method of accounting for goodwill and other intangible assets in 2002.

KPMG LLP

/s/ KPMG LLP

Shreveport, Louisiana
March 16, 2005