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**Exhibit 31.1 CERTIFICATION**

I, Karl F. Arleth certify that:

1.   I have reviewed this annual report on Form 10-K of Teton Petroleum Company;

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

3.   Based on my  knowledge,  the  financial  statements,  and  other  financial
     information included in this annual 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 annual 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 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 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  controls over financial  reporting,
     to the registrant's  auditors and the audit committee of 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  controls  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: March 29, 2005

/s/ Karl F. Arleth
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    Karl F. Arleth
    Chief Executive Officer
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