Abstract: In a laser beam cutting device the focussing of the laser beam (1) and the adjustment of the focal spot (4) in respect of its vertical position is made swing free, and is achieved without subsequent correction of the workpiece coordinates, with the focussing lens (2) guided strictly parallel and coaxial with the optical axis. By active cooling of the surface of the workpiece in the immediate area of the focal spot (4), the critical heating-up zone is reduced and the accuracy and surface finish of the cut edge is improved.