Abstract: In a laser beam machining method and a laser beam machining apparatus, a higher improvement in machining ability is required for grooving and cutting of a semiconducting material or a ceramic material. In order to meet this requirement, the invention provides a laser beam machining apparatus and a laser beam machining method in which an ultraviolet laser beam is irradiated in pulses onto a workpiece made of an inorganic material to groove or cut the workpiece. In this laser beam machining apparatus and laser beam machining method, as the scanning speed of the ultraviolet laser beam is higher, or as the machining depth of the grooving or the cutting is greater, the pulse width of the ultraviolet laser beam is set to be greater. This can significantly improve the machining ability compared with a case where the average power is increased.