PURPOSE: To improve cutting efficiency and reduce the cutting cost by performing the cutting while adding the specific quantity of a powdery element producing the oxide being apt to sublimate or its compound in assist oxygen gas.

CONSTITUTION: At the time of cutting by laser beam gas, the cutting is performed while adding >10mg/sec of a powdery element producing the oxide being apt to sublimate or its compound in assist oxygen gas. However, since there is the possibility that the converging characteristic, etc., of the laser beam are impeded by a large quantity of adding the element, an upper limit is set to almost 20g/sec. A substance having such a property is a compound of, for instance, WC, W2C, Mo2C, CaCO3, etc., and a simple substance of W Mo, etc. Also, it is desirable to use grain powder with a grain size of almost 100 to 250 mesh. Consequently, the attachment of dross can be prevented in the case of cutting a thick plate by laser beam gas.