EXHIBIT 31.1

                    Certification of Chief Executive Officer
            Pursuant to Section 302 of the Sarbanes-Oxley Act of 2002


I, Robert G. Dutcher, certify that:

     1.   I have reviewed this quarterly report on Form 10-Q of Possis Medical,
          Inc. (Possis Medical);

     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 Possis Medical as of, and for, the periods presented in
          this quarterly report;

     4.   Possis Medical'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)) and internal
          control over financial reporting (as defined in Exchange Act Rules
          13a-15(f) and 15d-15(f)) for Possis Medical 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
               Possis Medical, 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.   Designed such internal control over financial reporting, or
               caused such internal control over financial reporting to 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 Possis Medical'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 Possis Medical's internal
               control over financial reporting that occurred during Possis
               Medical's most recent fiscal quarter (Possis Medical's fourth
               fiscal quarter in the case of an annual report) that has
               materially affected, or is reasonably likely to materially
               affect, Possis Medical's internal control over financial
               reporting; and

     5.   Possis Medical's other certifying officer and I have disclosed, based
          on our most recent evaluation of internal control over financial
          reporting, to Possis Medical's auditors and the audit committee of
          Possis Medical's board of directors (or persons performing the
          equivalent function):

          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 Possis Medical'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 Possis Medical's
               internal control over financial reporting.


Date: March 12, 2006                       By: /s/ Robert G. Dutcher
                                               ---------------------------------
                                                 ROBERT G. DUTCHER
                                                 Chairman, President and
                                                 Chief Executive Officer


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