There are disclosed novel, solid, elastomeric block copolymers with improved resistance to cold flow wherein either 1) the terminal blocks are each a polymer (I polymer) of at least one conjugated diene (I), e.g., isoprene, which contains at least five carbon atoms with at least one of each pair of double-bonded carbon atoms in the polymerized diene I units being additionally single-bonded to two carbon atoms; at least one middle or interior block is a hydrogenated polybutadiene (B polymer); and at least one middle or interior block is an essentially straight chain polyethylene (E polymer) resulting from the hydrogenation of a polybutadiene composed of at least 80 % of 1,4- units; or 2) the terminal blocks are random copolymers resulting from the hydrogenation of a copolymer of at least one diene I as previously defined and hydrogenated butadiene, and at least one middle or interior block is a straight chain polyethylene (E polymer) as previously defined. The hydrogenated butadiene units in the B polymer or random IB polymer blocks are composed of no more than about 65 % of 1,4- units and at least about 35 % of 1,2- units. The foregoing block copolymers may be prepared by selectively hydrogenating substantially all the butadiene units of a precursor block, copolymer wherein the precursor blocks of the straight chain polyethylene block units are polybutadiene blocks in which at least about 80 % of the butadiene units are 1,4- units. A sufficient number of I units in the I polymer blocks or random IB copolymer blocks retain their unsaturation on selective hydrogenation to enable the vulcanization of the block copolymer.