There is disclosed a pneumatic tire having a rubber component comprising a sulfur cured rubber composition composed of, based on 100 parts by weight of rubber (phr): (a) 99 to 50 parts by weight of a first rubber containing olefinic unsaturation; and (b) 1 to 50 parts by weight of a second rubber which is different from said first rubber and which is an elastomeric block copolymer of (1) from 15 to 65 percent by weight, based on the total block copolymer, of butadiene, and (2) from 35 to 85 percent by weight, based on the total block copolymer, of styrene, which block copolymer has: (a) at least two blocks A which have polymerized units of styrene, a glass transition temperature Tg above 25null C. and forms a rigid phase, and (b) at least one elastomeric block which is composed of about 25 to 70 percent by weight of butadiene and 75 to 30 percent by weight of styrene, and which has polymerized B/A units of styrene and butadiene in a random structure; a glass transition temperature Tg from null50null C. to 25null C., and is located between two blocks A and forms a flexible phase, and the amount of the rigid phase accounts for 5 to 40 percent by volume.