To provide a pressing method for expanding local area thickness which enables the wall thickness dimension in a corner section corresponding to a root section to relatively increase at the time of press-forming a deep- dishlike or a cuplike molding by the perpendicular forming of a flange section.

In the upset forming which upsets the flange section 2 formed in the former process in the height direction, a radius of curvature in the outer side curvature surface 5B of the corner section 5 is formed smaller than the regular radius of curvature required for the molding, and the wall thickness dimension T of the corner section 5 increases the thickness of other regions (Fig. (A)-(C)). In the secondary forming succeeding to the upset forming (Fig. 8 (D)), the radius of curvature in the outer side curvature surface 5b of the corner section 5 is impressed so as to set the regular radius of curvature, but the thickness dimension T increased can be maintained.