A method for manufacturing molded articles with cores uses a 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 movable and capable either of moving together or sliding with respect to one another. Molding materials are supplied for a core and an outer layer. 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.