Methods for manufacturing panel units may include applying a cover tape to a surface of a panel in such a way as to substantially extend along a periphery of the panel. An extrusion molding die may be moved relative to the panel in such a way that the extrusion molding die moves along the periphery of the panel while at least partially contacting the cover tape applied to the panel. At the same time, a molten molding material may be extruded from the extrusion molding die, thereby integrally forming a molded article on the periphery of the panel. The cover tape may be then removed from the surface of the panel in order to produce a panel unit having the molded article disposed along the periphery of the panel.