A 2-stage plate forging process consisting of drawing and compression of tailored blanks having local thickening for the deep drawing of square cups was developed. A sheet having uniform thickness is drawn into a cup having a flange, and then is compressed with a punch and a flat die under fixture of edges of the flange to thicken the inclined portions. The degree of thickening was increased by controlling the punch stroke in the drawing stage, because the degree of thickening is small for a small stroke and folding occurs for a large stroke. The tailored blank having local thickening was drawn into a square cup. The limiting height of the drawn cup without fracture using the tailored blank was increased to 34 mm, whereas the height limit using the uniform blank was 18 mm. The limiting height of the cups for the tailored blanks formed by the drawing-compression having the 2 stages was almost similar to that formed by the bending-compression having the 4 stages, because the regions except for the target ones are thickened for the bending-compression. 2 shock lines appearing in the tailored blank were eliminated with a counter punch in the compression stage.