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EX-99.906CERT


                                 EXHIBIT 12 (b)
                           RULE 30a-2(b) CERTIFICATION

         In connection with the report of Cohen & Steers Institutional Realty
Shares, Inc. (the "Company") on Form N-CSR as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), I, Adam M. Derechin,
Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. 'SS'1350,
as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of
the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.


                                                   /s/ Adam M. Derechin
                                                   --------------------
                                                   Adam M. Derechin
                                                   Chief Executive Officer
                                                   Date: August 23, 2005





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                                 EXHIBIT 12 (b)
                           RULE 30a-2(b) CERTIFICATION

          In connection with the report of Cohen & Steers Institutional Realty
Shares, Inc. (the "Company") on Form N-CSR as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), I, Jay. J. Chen, Chief
Financial Officer of the Company, certify, pursuant to 18 U.S.C. 'SS'1350, as
adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of
the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.

                                            /s/ Jay J. Chen
                                            -----------------------
                                            Jay J. Chen
                                            Chief Financial Officer
                                            Date: August 23, 2005