<PAGE>

                                CERTIFICATION

                                                                Exhibit 31.1
                                                                ------------

I, Zsolt Rumy, certify that:

1.   I have reviewed this quarterly report on Form 10-Q of Zoltek Companies,
     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(s) 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)) and internal
     control over financial reporting (as defined in Exchange Act Rules
     13a-15(f) and 15d-15(f)) 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 quarterly report is being prepared;

     (b) Designed such internal control over financial reporting, or caused
         such internal control over financial reporting to be designed under
         our supervision, to provide reasonable assurance regarding the
         reliability of financial reporting and the preparation of financial
         statements for external purposes in accordance with generally
         accepted accounting principles;

     (c) 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

     (d) 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(s) 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 9, 2006

By: /s/  Zsolt Rumy
    -------------------------
    Zsolt Rumy
    Chief Executive Officer