The invention relates to a machine tool for the machining, particularly for the machining by turning and milling, of work pieces (25) having a centric bore (251), having a tool holder (19, 22) for holding a tool (23), a work piece support (13) for supporting the work piece (25), a work piece mount (30) for fixing the work piece (25), and a drive means (33) for turning the work piece (25) about a centric rotational axis (35). In order to be able to machine work pieces (25) intended for operation at a very high rotational speeds with high precision such that balancing after machining can preferably be completely eliminated, the invention provides that the work piece support (13) comprises a mandrel (36) for attaching the work piece (25) such that a section of the mandrel (36) projects into the bore (251) on a first side (252) of the work piece (25), and that the work piece support (30) has a counter holder (30) that can be moved in the direction of the bore axis (255) of the centric bore (251) for applying a pressing force onto the work piece (25) acting in the direction of the bore axis (255) on a second side (250) positioned opposite the first side (252).