<PAGE>
                                                                    Exhibit 31.1

               CERTIFICATION PURSUANT TO RULE 13A-14(a)/15D-14(a),
                             AS ADOPTED PURSUANT TO
                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002

I, David D. Stevens, certify that:

1.  I have reviewed this annual report on Form 10-K of Accredo Health,
    Incorporated;

2.  Based on my knowledge, this 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 report;

3.  Based on my knowledge, the financial statements, and other financial
    information included in this 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 report;

4.  The registrant's other certifying officer 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 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 report is being
      prepared;

           (b) 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

           (c) 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 (the registrant's fourth fiscal quarter in the
      case of an annual report) 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:

           (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
      control over financial reporting.


Date:  September 13, 2004
                                                   /s/ David D. Stevens
                                                   -----------------------------
                                                   David D. Stevens
                                                   Chief Executive Officer