Provided is a method of producing a resin molded article which hardly involves the occurrence of optical distortion and of sink marks. The method of producing a resin molded article includes: a first step including pouring a polyfunctional (meth)acrylic monomer into a molding die and irradiating the polyfunctional (meth)acrylic monomer with radiant energy rays until a polymerization conversion degree reaches 1 to 10% to polymerize a part of the polyfunctional (meth)acrylic monomer; and a second step including heating the polymerized polyfunctional (meth)acrylic monomer after the first step in a state where the polymerized polyfunctional (meth)acrylic monomer is held in the molding die to further polymerize a remaining part of the polyfunctional (meth)acrylic monomer until the polymerization conversion degree reaches 60% or more.