Exhibit 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
                          PEOPLES FINANCIAL CORPORATION
                       PURSUANT TO 18 U.S.C. Section 1350

I, Chevis C. Swetman, Chairman, President and Chief Executive Officer of Peoples
Financial Corporation (the "Company"), hereby certify that the accompanying
report on Form 10-K for the period ending December 31, 2003 and filed with the
Securities and Exchange Commission on the date hereof pursuant to Section 13(a)
of the Securities Exchange Act of 1934 (the "Report") by the Company fully
complies with the requirements of that section.

I further certify that the information contained in the Report fairly presents,
in all material aspects, the financial operations and results of operations of
the Company.

BY: /s/ Chevis C. Swetman
    -----------------------------------------
    Chevis C. Swetman
    Chairman, President and Chief Executive Officer

DATE: March 24, 2004