PURPOSE: To eliminate thoroughly the damage on a material plate and to obtain a satisfactory cut surface by raising a working head in the part where the cutting route on the material plate is discontinuous.

CONSTITUTION: A working head of a laser cutting machine is provided freely vertically movably. A freely vertically movable tube part 3b is fastened 16 and fixed onto a base plate 14. The plate 14 is made freely slidable with the top end face of an upper frame 2a. Supporting bars 18 are suspended to the plate 14 and contact plates 19 are provided to the bottom end of the bars 18. The extent at which a torch part 24 projects downward is adjusted by the plates 19. The working head is raised and a shutter is closed to stop irradiation of laser light while a material plate W moves. When the start point for working the plate W is determined upon stopping of the moving device, the working head is lowered and the shutter is opened to irradiate the laser light and to start programmed cutting.