----

 

**Exhibit 31.1**

**Certifications**

I, Fred S. Zeidman certify that:

 
| 1.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | I have reviewed this quarterly report on Form 10-Q  of Seitel, 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 22, 2004

 

/s/ Fred S. Zeidman

Fred S. Zeidman

Principal Executive Officer

** **

  |