PURPOSE: To obtain the titled composition exhibiting improved service durability as a rubber cup with excellent anti-flatting property, by incorporating carbon black, a peroxide, and a crosslinking assistant into a specified copolymer rubber, followed by vulcanizing thereof.

CONSTITUTION: 15W70pts.wt. carbon black having particle diameters of 50μm or smaller, 0.1W5.0pts.wt. peroxide having a temperature to obtain a half-life of 1min of 175W200°C (e.g. di-t-butylperoxydiisopropylbenzene), and 0.01W5.0pts.wt. vulcanizing assistant (e.g. dipentamethylenethiuram) are incorporated into 100pts. wt. ethylene-propylene copolymer rubber or ethylene-propylene-conjugated diene terpolymer rubber, which is vulcanized at 140W220°C for 1W120min to obtain a rubber composition for a brake cylinder rubber cup, having a network chain content of 5×10-5W9×10-4mol/cc.