The invention relates to a device for holding an annular or disk-shaped workpiece on a machine tool. With this device, a particularly precise machining of the workpiece can be carried out on a plurality of surfaces. The device comprises a receiving upper part (4) and a receiving lower part (5), wherein the receiving upper part (4) and the receiving lower part (5) are connectable to each other coaxially with the central axis (a) in a detachable manner, the receiving upper part (4) has a plurality of actuating elements (6) with which radial (r) forces and/or radial displacements can be applied to the workpiece (2) respectively. The operating element (6) is manipulated by squeezing the pressurized fluid; in the receiving lower portion (5), a plurality of actuators (7) corresponding to the number of the operating elements (6) are arranged. With the actuator, a defined volume of pressurized fluid can be delivered to the respective transfer element (8).