PURPOSE: To obtain the title rubber composition, capable of enhancing insufficient tensile strength of unvulcanized rubber, having excellent molding processability and useful for tires, packings, etc., by blending unvulcanized rubber with a hydrogenated block copolymer and an acid-modified substance thereof.

CONSTITUTION: The aimed rubber composition, obtained by blending (A) 100 pts.wt. at least one of natural rubber, isoprene rubber, butadiene rubber, styrene- butadiene random copolymer rubber and butyl rubber with (B) 1W100 pts.wt. block copolymer consisting of (i) vinyl aromatic compound polymer blocks and (ii) olefinic compound polymer blocks and having an unsaturation degree without exceeding 20% and/or a modified block copolymer having molecular units, containing carboxylic acid groups or derivative groups linked thereto, (C) a vulcanizing agent and, as necessary, (D) an additive, such as filler or softener, having a high green strength and excellent mechanical properties as rubber after vulcanization.