An apparatus for machining a planar metal workpiece, having at least one machining unit, with which a machining belt, which is driven in circulation, can be guided in an at least approximately linear manner past the region of the workpiece to be machined in an oblique or transverse manner with respect to a feed direction of the workpiece. A movable carrier element having pressure means acts on a rear side of the machining belt in order to influence contact, necessary for machining, between the working side of the machining belt and the workpiece. A drive arrangement, by way of which the carrier element can be motor-driven, is provided such that the carrier element moves substantially parallel to the direction of movement of the machining belt, at least in the working region of the machining belt.