Abstract: The disclosed method for deburring and chamfering a burred sharp edge, which is defined between two transversely extending sides of workpiece, includes forming a molten pool of material on one of the sides by a laser beam which wobbles transversely to the burred edge. The wobbling amplitude of the laser beam is controlled so that the oscillating beam is prevented from being guided beyond the edge. The heat generated by the molten material is transferred to and liquefies the burrs. As the molten material cools and solidifies, it pools on the surface of the workpiece forming a raised smootcurved surface layer which chamfers the edge.