Abstract: A machine for cutting grooves in workpieces, particularly in sheet form, having at least one fixed cutter, support means for supporting the workpiece against the cutter and means for moving the workpiece relative to the cutter and support means. The cutter has a cutting edge defining the shape of groove to be cut and is arranged to slice through the workpiece to produce a groove leaving a constant thickness of material between the bottom of the groove and the other side of the workpiece. The forces tending to lift the workpiece from its support due to the action on the cutter of material removed thereby are overcome and a resultant force operating to press the workpiece on to its support is produced by arranging, either singly or in combination, thatA. the cutter has a cutting edge substantially contained in a plane which extends forwardly in the direction of relative movement of the cutter and upwardly of the surface of the workpiece,B.