<PAGE>

                                                                    Exhibit 31.1

                                  CERTIFICATION

I, Thomas P. Richards, certify that:

1.       I have reviewed this annual report on Form 10-K of Grey Wolf, 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)      [paragraph omitted pursuant to SEC Release Nos. 33-8238 and
                  34-47986];

         (c)      evaluated the effectiveness of the registrant's disclosure
                  controls and procedures presented in this annual report our
                  conclusions about the effectiveness of the disclosure controls
                  and procedures, as of the end of the period covered by this
                  annual report based on such evaluation; and

         (d)      disclosed in this annual report any change in the registrant's
                  internal control over financial reporting that occurred during
                  the registrant's quarter ended December 31, 2003 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: February 12, 2004                By: /s/ Thomas P. Richards
                                           -------------------------------------
                                           Thomas P. Richards
                                           Chairman, President and Chief
                                           Executive Officer