<PAGE>

                                                                    EXHIBIT 31.1

                            CERTIFICATION PURSUANT TO
            RULE 13a-14(a) UNDER THE SECURITIES EXCHANGE ACT OF 1934

      I, Gary Lemke, Chief Executive Officer of A.S.V., Inc., certify that:

      1.    I have reviewed this Quarterly Report on Form 10-Q of A.S.V., Inc.;

      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 (or persons performing the equivalent
functions):

            (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: November 9, 2004

                                         /s/ Gary Lemke
                                         ---------------------------------------
                                         Gary Lemke
                                         Chief Executive Officer

                                       22