To provide a method an apparatus for press forming, which has the degree of freedom of excellent die design and controls the generation of wrinkles on the outside wall surface of a curved portion of a part having an opened cross section.

This apparatus has a punch corresponding to the internal shape of the part, a die which is arranged freely approachably and separably to and from the punch and corresponded to the external shape of the part and a die carving part 174A which is arranged on the surface 170 of the die face of the die. The die carving part 174A has an guiding part 175 and a relief part 176 which is continuously connected to the guiding part 175. The guiding part 175 which is located on the die face surface 184 corresponding to the outside wall surface of the curved part of the part and guides the surplus material of a metal plate 100 composing the outside wall surface toward the relief part 176. The material guided by the guiding part 175 is introduced to the relief part 176.