The wall thickness around an inner corner of 3-stage-formed cups with a flange was increased using conical punches in the 1st and 2nd stages. Since the strength of the formed cups is greatly improved by increasing the wall thickness, the weight of the formed products is reduced by an optimum distribution of the wall thickness resulting from the increase in wall thickness. The increase in thickness around the inner corner was achieved by compressing the side wall and the conical bottom of the cup using an outer punch in the 3rd stage. The amount of compression in the 3rd stage was expressed in terms of the drawn volume after the 2nd stage, and the drawn volume was optimized. Although the maximum increase in wall thickness around the inner corner for the conical punches of 25^o was about 9% that with the flat punches, the maximum forming load with the conical punches decreased by about 30%.