EX-99.906CERT

                                 EXHIBIT 10 (b)
                          RULE 30a-2(b) CERTIFICATIONS

     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, Robert H. Steers,
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/ Robert H. Steers
                                         ---------------------------------------
                                         Robert H. Steers
                                         Chief Executive Officer
                                         Date: February 27, 2004






                                 EXHIBIT 10 (b)
                          RULE 30a-2(b) CERTIFICATIONS

     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, Martin Cohen, 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/ Martin Cohen
                                         ---------------------------------------
                                         Martin Cohen
                                         Chief Financial Officer
                                         Date: February 27, 2004