Abstract: In a machine tool for abrasive machining of planar surfaces having a bed (1) supporting a workhead (28), a faceplate (9) carrying an abrasive tool (11), which is mounted for rotation by means of a thrust bearing (13) on an annular support (12) attached to the bed (1) and which is rotated by a coaxial drive shaft (3) journalled in antifriction bearings (16), and an adjustable means for pressing the faceplate (9) against the annular support (12), comprising an air-powered diaphragm (21) having a hollow rod (15) through which extends the drive shaft (3), according to the invention, the annular support (12) has a coaxial bushing (14) in which the hollow rod (15) is mounted for axial movement and to which a casing (22) of the air-powered diaphragm (21) is attached, the antifriction bearings (16) of the drive shaft (3) being mounted in the hollow rod (15) and the drive shaft (3) being coupled to the faceplate (9) by means of an elastic member (8).