Block copolymer composition, method for producing the same, and film of the same

A block copolymer composition comprising an aromatic vinyl-conjugated diene-aromatic vinyl block copolymer having a high-level balance between a high elastic modulus and a small elongation set is provided. The block copolymer composition comprises a block copolymer A represented by formula (A) and a block copolymer B represented by formula (B), where the weight ratio of the block copolymer A to the block copolymer B, A/B, is from 36/64 to 85/15 and the ratio of the aromatic vinyl monomer units relative to all polymer components in the block copolymer composition is 27-70 wt %. Ar1a-Da-Ar2a (A). Ar1b-Db-Ar2b (B). (In the formulae, Ar1a, Ar1b and Ar2b each represent an aromatic vinyl polymer block having a weight-average molecular weight of from 6,000 to 18,000; Ar2a represents an aromatic vinyl polymer block having a weight-average molecular weight of from 40,000 to 400,000; Da and Db each represent a conjugated diene polymer block having a vinyl bond content of from 1 to 20% by mol; and Db has a weight-average molecular weight of from 60,000 to 400,000).