EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
     PURSUANT TO RULE 13A-14(B) OR RULE 15D-14(B) AND 18 U.S.C. SECTION 1350

In connection with the Annual Report on Form 10-K of The Meridian Resource
Corporation (the "Company") for the year ended December 31, 2004, as filed with
the Securities and Exchange Commission on the date hereof (the "Form 10-K"), I,
Joseph A. Reeves, Jr., Chief Executive Officer of the Company, certify pursuant
to Section 906 of the Sarbanes-Oxley Act of 2002, that:

     1.   The Form 10-K fully complies with the requirements of Section 13(a) or
          15(d) of the Securities Exchange Act of 1934; and

     2.   The information contained in the Form 10-K fairly presents, in all
          material respects, the financial condition and results of operations
          of the Company.

Date: March 15, 2005


                                        /s/ Joseph A. Reeves, Jr.
                                        ----------------------------------------
                                        Joseph A. Reeves, Jr.
                                        Chief Executive Officer