The present invention provides a novel epoxy resin-based curable composition suitable for use as an encapsulating resin composition for semiconductor devices capable of being highly resistant against crack formation with low internal stress by curing and yet having very high heat conductivity and maintaining high glass transition temperature. The inventive composition comprises (a) 100 parts by weight of a curable epoxy resin blend which is a mixture of an epoxy resin and a curing agent therefor, (b) from 5 to 100 parts by weight of a block copolymer composed of at least one segment of an aromatic polymeric moiety, phenyl novolac, and at least one segment of an organopolysiloxane moiety having 30 to 200 silicon atoms and bonded to the aromatic polymeric moiety through a carbon-to-silicon linkage, and optionally (c) an inorganic filler which is preferably a silica filler such as powdered quartz in an amount not exceeding 1000 parts by weight.