A curable resin composition comprising not only at least one addition polymerization block copolymer (I) selected from among block copolymers, the block copolymers each having at least one polymer block A composed mainly of aromatic vinyl compound units containing at least 1 mass% of structural units (a) derived from an alkylstyrene comprising a benzene ring having at least one alkyl of C1-C8 bonded thereto and at least one polymer block B composed mainly of conjugated diene compound units wherein at least the moiety of polymer block A can be crosslinked by actinic energy radiation, and products of hydrogenation of the block copolymers but also ethylenically unsaturated compound (II); and a flexographic plate material comprising the curable resin composition as a constituent thereof. The flexographic plate material comprising the above curable resin composition as a constituent thereof, especially in the printing on a matter of rough surface to be printed, such as a cardboard or recycled paper, excels in the strength and elongation of cured portions and provides a plate surface with sharp image even at the formation of fine image area.