In a metal plate material hot molding apparatus for press molding a heated metal plate material (1), supply piping (6) for a cooling medium is provided in a mold (2, 3), and ejection holes (4) penetrating from a molding surface of the mold (2, 3) to the supply piping (6) are provided. Discharge piping (7) for the cooling medium may be provided in the mold (2, 3), and discharge holes (5) penetrating from the molding surface of the mold (2, 3) to the discharge piping (7) may be provided, and further, cooling piping (8) may be provided. Molding is performed while the cooling medium is ejected from the ejection holes (4) to a gap between the metal plate material (1) and the mold (2, 3).