Abstract: A machine for forming rotationally symmetrical workpieces includes a base on which is mounted a roller head carrier for a roller head, particularly a multi-roller head having for example three shaping rollers which are arranged at an angular spacing of 120.degree.. The base further supports a headstock which carries the tool for the workpiece to be shaped and a pressing tail spindle for a counterholder which is associated with the workpiece for pressing same against the tool. The roller head carrier and the headstock interconnect through a feed drive for driving the shaping rollers along the workpiece by relative movement of the roller head carrier and head stock. One of the roller head carrier and head stock is connected to the base and the other one is movably guided on the base. The roller head carrier projects on the side of the roller head facing the headstock and has a recess which extends longitudinally of the machine.