PURPOSE: To provide a rubber compsn. having well-balanced vibration-proofness and soundproofness, by blending carbon black with a rubber contg. a polymer obtd. by grafting an unsaturated dicarboxylic acid onto a diene rubber, and vulcanizing the mixture with sulfur.

CONSTITUTION: A vibration-proof, soundproof rubber compsn. is obtd. by blending 5W60pts.wt. carbon black with 100pts.wt. rubber contg. at least 40wt% polymer obtd. by grafting 0.001W10pts.wt. unsaturated dicarboxylic acid (derivative), such as maleic acid (anhydride), onto at least one rubber selected from diene rubbers such as polybutadiene and diene copolymer rubbers such as a butadiene/ styrene copolymer, and then vulcanizing the mixture with sulfur. Heretofore, no polymer which simultaneously satisfies both vibration-proofness and soundproofness is discovered as yet. However, by the above blending, a polymer having similtaneously the both characteristics can be obtd, and said polymer is suitable for use as automobile engine mount.