Abstract: In the shaping of ductile metal sheet, especially superplastic alloy sheet, by the application of pressure differentials, the peripherally clamped sheet is first urged, by pressure differential in one direction, against a female molding surface to form a partially shaped bubblelike preform and then a male mold is advanced towards the sheet from the other side and a reverse pressure differential is applied to cause the pre-form to conform to the shape of that mold. The active area forming the pre-form may be restricted by an apertured plate adjacent the clamping plane, matching the overall outline of the body, and a plate the other side matching closely the profile of the body may confine the action of the reverse pressure only to that part of the sheet that engages the progressively increasing part of the male mold that extends through the clamping plane so that the sheet locks progressively onto the sides of the male mold to obtain an approximately uniform wall thickness in the finished body.