Abstract: Disclosed is a device for machining a workpiece transportable in a chosen direction in accordance with a selected pattern by a focussed laser beam. The device includes a scanner with a converging optical system. The scanner has a chosen distance relative to the workpiece. On the basis of the maximum laser output there is defined on the workpiece a certain operating area, of which the linear dimension transversely of the transporting direction is small relative to the dimension transversely of the workpiece. The device further includes computer-controlled displacing device for displacing the scanner substantially perpendicularly of the chosen direction. The scanner is displaced under computer control in transverse direction relative to the longitudinal movement of the workpiece. The machining takes place during the displacement of the scanner. The displacement speed is continuously adjusted to the amount of work available within the operating area of the scanner.