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Exhibit 31.1 CERTIFICATION OF CHIEF EXECUTIVE OFFICER
PEOPLES FINANCIAL CORPORATION
PURSUANT TO SECTION 302 OF THE
SARBANES-OXLEY ACT OF 2002 I, Chevis C. Swetman, certify that: 1. I have reviewed this quarterly report on Form 10-Q of Peoples Financial
Corporation. 2. Based on my knowledge, the report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by the report; 3. Based on my knowledge, the financial statements, and other financial
information included in the report, fairly present in all material respects the
financial condition, results of operation and cash flows of the registrant as
of, and for, the periods presented in the report; 4. The registrants other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as such term
is defined in Exchange Act Rules 13a-15(e) and 15d-15(e) and internal control
over financial reporting (as defined in Exchange Act Rules 13a-15(f) and
15d-15(f)) for the registrant and have: a) designed such disclosure controls and procedures or caused such
disclosure controls and procedures to be designed under our supervision
to ensure that material information relating to the registrant, including
its consolidated subsidiaries, is made known to us by others within those
entities, particularly during the period in which the periodic reports
are being prepared; b) designed such internal control over financial reporting or caused such
internal control over financial reporting be designed under our
supervision, to provide reasonable assurance regarding the reliability of
financial reporting and the preparation of financial statements for
external purposes in accordance with generally accepted accounting
principles; c) evaluated the effectiveness of the registrants disclosure controls
and procedures and presented in this report our conclusions about the
effectiveness of the disclosure controls and procedures as of the end of
the period covered by this report based on such evaluation; and d) disclosed in this report any change in the registrants internal
control over financial reporting that occurred during the registrants
most recent fiscal quarter that has materially affected, or is reasonably
likely to materially affect, the registrants internal control over
financial reporting. 5. The registrants other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrants auditors and the audit committee of




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the registrants board of
directors (or persons performing the equivalent functions): a) all significant deficiencies and material weakness in the design or
operation of internal control over financial reporting which are
reasonably likely to adversely affect the registrants ability to record,
process, summarize and report financial data; and b) any fraud, whether or not material, that involves management or other
employees who have a significant role in the registrants internal
controls; and Dated: November 10, 2004 /s/ Chevis C. Swetman