A forming device for cup-shaped hollow bodies having a machine frame, a drive device, a workpiece rotary table for accommodating hollow bodies and a tool holder for accommodating processing tools, wherein the workpiece rotary table and the tool holder face one another and can be turned about a rotational axis in relation to one another and can be linearly moved in relation to one another along the rotational axis, and wherein the drive device comprises first drive means for providing a rotary step movement and second drive means for providing a cyclical linear movement between workpiece rotary table and tool holder to enable the hollow bodies to be formed by means of the processing tools in a plurality of consecutive processing steps. The second drive means has a stroke adjustment arrangement which is designed for adjusting a working stroke of the cyclical linear movement as a function of a control signal of a control device and/or for continuously variably adjusting the working stroke.