In casting, molding and forming processes, the surface geometries of the fabricated products are formed/molded by different functional components of tooling. In plastic injection molding, they are molded by core, cavity or side-cores. In die and mold CAD, how to identify the product surfaces formed/molded by the corresponding tool components for a given product CAD model is critical, as it affects the determination of parting directions, parting lines and parting surfaces, the generation of core and cavity blocks, and finally the design of side-cores and their actuating mechanisms. In this paper, the concepts of surface visibility, demoldability, and moldability are first presented and formulated. The surfaces formed/molded by core, cavity and side-cores are then defined based on the plastic injection molding process. The methodology to identifying and classifying them is further developed. By employing the proposed notions of the demoldability map of surfaces and undercut features, the most preferred demolding direction, the grouping of undercut features, and how to conduct the side-core design is articulated succinctly, and the detailed procedures and processes are presented. Through an industrial case study, the developed methodology for side-core design is systematically presented and the feasibility of the developed approaches is verified.