Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER
PEOPLES FINANCIAL CORPORATION
PURSUANT TO 18 U.S.C. ss. 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-Q for the period ending September 30, 2004 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
	November 10, 2004
	Date