Exhibit 31.1**CERTIFICATION**I, Thomas P. Richards, certify that:1. I have reviewed this quarterly report on Form 10-Q of Grey Wolf, Inc; 2. Based on my knowledge, this report does not contain any untrue statement of a material factor omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this report; 3. Based on my knowledge, the financial statements, and other financial information included inthis report, fairly present in all material respects the financial condition, results ofoperations and cash flows of the registrant as of, and for, the periods presented in thisreport; 4. The registrant’s other certifying officer and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the registrant and have: (a) designed such disclosure controls and procedures, or caused such disclosurecontrols and procedures to be designed under our supervision, to ensure that materialinformation relating to the registrant, including its consolidated subsidiaries, ismade known to us by others within those entities, particularly during the period inwhich this report is being prepared;  (b) designed such internal control over financial reporting, or caused suchinternal control over financial reporting to be designed under our supervision, toprovide reasonable assurance regarding the reliability of financial reporting and thepreparation of financial statements for external purposes in accordance with generallyaccepted accounting principles;  (c) evaluated the effectiveness of the registrant’s disclosure controls andprocedures and presented in this report our conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by this reportbased on such evaluation; and  (d) disclosed in this report any change in the registrant’s internal control overfinancial reporting that occurred during the registrant’s quarter ended June 30, 2005that has materially affected, or is reasonably likely to materially affect, theregistrant’s internal control over financial reporting; and5. The registrant’s other certifying officer and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and theaudit committee of the registrant’s board of directors (or persons performing the equivalentfunctions): (a) all significant deficiencies and material weaknesses in the design or operationof internal control over financial reporting which are reasonably likely to adverselyaffect the registrant’s ability to record, process, summarize and report financialinformation; and  (b) any fraud, whether or not material, that involves management or other employeeswho have a significant role in the registrant’s internal control over financialreporting.     Date: August 4, 2005 By: /s/ Thomas P. Richards         Thomas P. Richards    Chairman, President and Chief Executive Officer