A device for high-precision machining of the surface of an object, such as for polishing and lapping semiconductor substrates, in which the object is held on an accommodation surface for its machining. The accommodation surface can be deformed by means of a actuators connected to the surface in a positive-lock and/or non-positive-lock manner. The actuators are provided between a base plate and an accommodation plate that are mechanically biased relative to one another. The accommodation plate is configured, on its inside, with concentric grooves forming rigid rings in the axial direction. The individual rings are connected by solid substance joints. Piezo-stacks configured as actuator-sensor elements, as well as springs, are disposed between the faces of the rings and the base plates and are offset relative to one another by 120.degree..