A composition for photosensitive flexographic plates which is capable of forming a sheet having a smooth surface and excellent antiflowing properties and less apt to have trouble caused by sticking and which further has excellent thin-line reproducibility; a block copolymer composition for photosensitive flexographic plates which is suitable for use in the composition; and a flexographic plate obtained by exposing the composition to light. Also provided are: a block copolymer composition containing a three-branched aromatic vinyl/conjugated diene block copolymer obtained with a specific coupling agent; and a composition for photosensitive flexographic plates which comprises an ethylenic compound and a photopolymerization initiator.