A forming device for cup-shaped hollow bodies (56) with a machine frame (2), a drive mechanism (6), a workpiece turntable (3) to support hollow bodies (56) and a tool carrier (4) to support machining tools (58), wherein the workpiece turntable (3) and tool carrier (4) oppose one another and can be rotated in relation to one another around an axis of rotation (5) and can be linearly displaced in relation to one another along the axis of rotation (5) and wherein the drive mechanism (6) is designed to provide a rotational stepping motion and a cyclical linear motion between the workpiece turntable (3) and the tool carrier (4), in order to allow the forming of the hollowing bodies (56) by means of the machining tools (58) in a plurality of sequential machining steps, as well as a stationary supporting tube (33) assigned to the machine frame (2), the central axis of which extends along the axis of rotation (5) and supports the tool carrier (4) and/or the workpiece turntable (3). On an external surface (36) of the supporting tube (33) a guiding device (40) is arranged, which is designed for the mounting with a linear motion of the tool carrier (4) and/or the workpiece turntable (3) on the supporting tube (33).