A resin composition for sealing semiconductors which comprises (a) an epoxy resin, (b) a hardening agent, (c) an inorganic filler and (d) a polymaleimide having a specific structure is herein provided. Preferably, the resin composition comprises, as all of or a part of the epoxy resin, a modified epoxy resin composed of (i) a graft polymer of an epoxy resin and a vinyl polymer and (ii) a silicone polymer in an oily state or as particles having an average particle size of not more than 1.0 micron, which are uniformly dispersed in the graft polymer. The resin composition for sealing semiconductors exhibits a low thermal expansion coefficient and a low elastic modulus, generates low stress when thermal shock is applied thereto and exhibits high heat resistance during soldering even after moisture absorption. Therefore, if the composition is used to seal semiconductor devices on a large scale having degree of integration or small-sized, thin semiconductors such as flat packages, these semiconductors provide high reliability.