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                                                                   EXHIBIT 10.31

                             URANIUM RESOURCES, INC.

                           CERTIFICATE OF AMENDMENT OF
                      RESTATED CERTIFICATE OF INCORPORATION


         The undersigned, Paul K. Willmott, the duly elected and acting
Chairman, Chief Executive Officer and President of Uranium Resources, Inc., a
Delaware corporation (the "Corporation"), does hereby certify as follows:

         First: That the Board of Directors of the Corporation, in accordance
with Section 242 of the Delaware General Corporation Law adopted resolutions
setting forth a proposed amendment of the Restated Certificate of Incorporation
of the Corporation, declaring said amendment to be advisable and calling for the
stockholders of the Corporation to consider said amendment at the next Annual
Meeting of the Stockholders, to be held on June 18, 1999.

         Second: That thereafter, upon notice in accordance with Section 222 of
the Delaware General Corporation law, the Annual Meeting of the Stockholders was
held on June 18, 1999 and, at that meeting, the necessary number of shares as
required by statute were voted in favor of the amendment.

         Third: That amendment deletes Article 4 of the Restated Certificate of
Incorporation in its entirety and replaces Article 4 of the Restated Certificate
of Incorporation with the following:

                                    ARTICLE 4

         The aggregate number of shares which the corporation has authority to
issue is Thirty-Five Million (35,000,000) shares, $.001 par value per share. The
shares are designated as common stock and have identical rights and privileges
in every respect. The holders of the stock of the corporation shall have no
preemptive rights to subscribe for any securities of the corporation.

         Fourth: That said amendment was duly adopted in accordance with the
provisions of Section 242 of the Delaware General Corporation Law.

         IN WITNESS WHEREOF, the undersigned has executed this Certificate on
June 22, 1999.

                                           /s/  Paul K. Willmott
                                           -------------------------------------
                                           Paul K. Willmott, Chairman,
                                           Chief Executive Officer and President