<PAGE>

                                                                    EXHIBIT 31.1

                            CERTIFICATION PURSUANT TO
                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002

I, Lance F. Bospflug, certify that:

      1.    I have reviewed this quarterly report on Form 10-Q of Petroleum
            Helicopters, Inc.

      2.    Based on my knowledge, this quarterly 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 this quarterly report;

      3.    Based on my knowledge, the financial statements, and other financial
            information included in this quarterly report, fairly present all
            material respects the financial condition, results of operations and
            cash flows of the registrant as of, and for, the periods presented
            in this quarterly report;

      4.    The registrant's other certifying officers and I are responsible for
            establishing and maintaining disclosure controls and procedures (as
            defined in Exchange Act Rules 13a-14 and 15d-14) for the registrant
            and we have:

            a)    designed such disclosure controls and procedures 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 this quarterly report is being prepared;

            b)    evaluated the effectiveness of the registrant's disclosure
                  controls and procedures as of a date within 90 days prior to
                  the filing date of this quarterly report (the "Evaluation
                  Date"); and

            c)    presented in this quarterly report our conclusions about the
                  effectiveness of the disclosure controls and procedures based
                  on our evaluation as of the Evaluation Date;

      5.    The registrant's other certifying officers and I have disclosed,
            based on our most recent evaluation, to the registrant's auditors
            and the audit committee of registrant's board of directors (or
            persons performing the equivalent function):

            a)    all significant deficiencies in the design or operation of
                  internal controls which could adversely affect the
                  registrant's ability to record, process, summarize and report
                  financial data and have identified for the registrant's
                  auditors any material weaknesses in internal controls; 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

      6.    The registrant's other certifying officers and I have indicated in
            this quarterly report whether or not there were significant changes
            in internal controls or in other factors that could significantly
            affect internal controls subsequent to the date of our most recent
            evaluation, including any corrective actions with regard to
            significant deficiencies and material weaknesses.

Date: May 7, 2004

By: /s/ Lance F. Bospflug
    --------------------------------
Lance F. Bospflug
President and Chief Executive Officer