Abstract: In a device for grinding workpieces, in particular workpieces made of ceramic materials, by means of a grinding wheel (24) or the like, the workpiece (23) is oscillated transversely to the machining direction during grinding. At least one ultrasonic transducer (1), whose ultrasonic energy is used as exciting energy for the workpiece (23), is provided as a device (20) for generating the oscillating movement of the workpiece (23). An ultrasonic resonance space (2,4) for amplitude transformation is provided between the ultrasonic transducer (1) and a sonotrode (5) which transmits the vibration to the workpiece (23).