In the deep-drawn molding of a plastic container, a molten plastic sheet is positioned between a plug and a mold. The molten sheet is supported on an upper mold surface portion having heat insulating property and slipperiness, and while a positive pressure is created between the mold and the molten sheet, the molten sheet is molded by moving the plug and the mold relative to each other in a closing direction. By drawing the molten sheet into the mold while allowing it to slide over the above upper mold surface portion, the amount of the molten plastic sheet drawn into the mold is increased, and a container can be produced which has a uniform height direction and a uniform thickness distribution in the container height direction and possesses good appearance characteristics without the occurrence of a drag line in its side wall.