Laser beam welding process in which the laser beam (10) generates a fusion zone within the workpiece with a welding cavity which is at least open towards the beam source during welding. To improve the process such that phenomena disturbing the welding process do not occur in the fusion zone, the laser beam is inclined such that it basically produces a vertical fusion front opposite to the relative direction of radiation. At low welding speeds in extreme conditions, for example overlock welding of coated plates, the laser beam is inclined in a different direction in order to generate a welding cavity which is wide open in the direction of the incident beam.