This invention is directed to provide a method of manufacturing a resin molded semiconductor device with high reliability by preventing a resin leakage portion from occurring due to burrs on a lead frame formed by punching. The method of manufacturing the resin molded semiconductor device according to the invention includes bonding a semiconductor die on an island in a lead frame, electrically connecting the semiconductor die with the lead frame, resin-molding the lead frame on which the semiconductor die is bonded, and applying prior to the resin-molding a compressive pressure that is higher than a clamping pressure applied in the resin-molding to a region of the lead frame being clamped by molds in the resin-molding of the lead frame.