A method for manufacturing a molded article with at one or more cores uses compression molding apparatus that includes upper and lower punches that have a double structure comprising a central punch and an outer punch that surrounds the periphery of the central punch. The central punch and the outer punch are capable of independent sliding motions and compressing operations. Molding materials are supplied for a core and an outer layer respectively. The molding materials are compressed by the punches to form molded articles that include the core. The method may be executed in a rotary compression molding machine.