<PAGE>

                                                                    Exhibit 31.1

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

I, Joseph F. Furlong, III certify that:

1.    I have reviewed this quarterly report on Form 10-Q of American
      HomePatient, 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 in 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-15(e) and 15d-15(e)) for the registrant
      and we 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 this quarterly report is being prepared;

      (b)   Evaluated the effectiveness of the registrant's disclosure controls
            and procedures and presented in this quarterly 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

      (c)   Disclosed in this report any change in the registrant's internal
            control over financial reporting that occurred during the
            registrant's first fiscal quarter that has materially affected, or
            is reasonably likely to materially affect, the registrant's internal
            control over financial reporting; and

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 the registrant's
      board of directors (or persons performing the equivalent functions):

<PAGE>

      (a)   All significant deficiencies and material weaknesses 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 information; 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 over financial reporting.

Date: May 6, 2004

                                            /s/ Joseph F. Furlong, III
                                            -----------------------------
                                            Joseph F. Furlong, III
                                            Chief Executive Officer