A hydrogenated nitrite rubber composition for providing a cross-linked product having a 20% modulus of 10 MPa or more and a thermal conductivity of 0.4 W/m·K or more at 25° C. The hydrogenated nitrile rubber composition includes 100 parts by weight of hydrogenated nitrile rubber having a bound acrylonitrile content of 40% or more, a polymer Mooney viscosity ML1+4 (100° C.) of 75 or less (median) as determined according to JIS K-6395, an iodine value of 23 or less (median), and at least 110 parts by weight in sum total of carbon black as a filler and other gas shielding filler. The hydrogenated nitrile rubber composition can effectively be used as a molding material for sliding applications or for a static sealing members for highly permeable gases. The hydrogenated nitrile rubber composition has a distinguishing carbon dioxide gas shieldability, heat resistance, and wear characteristics.