PURPOSE: To make possible fine cutting and to improve the production efficiency of a product by applying microoscillation to the melt-cut part of a thin sheet.

CONSTITUTION: A laser cutting torch 1 is disposed to the thin steel sheet 2 to be melt-cut and AC electromagnets 3, 3 are disposed on both sides of the melt-cutting part of the sheet 2. The sheet 2 is melt-cut by laser light 5 of the torch 1 while the force oscillation of the prescribed frequency and amplitude is applied to the electromagnets 3, 3'. The dross tending to stick to the melt-cut part 4 is sprung off by the microoscillation of the melt-cut part 4 or even if the dross sticks once thereto, the dross is splashed off at some size. The fine cutting of the part 4 is thus made possible and the production efficiency of the product to be used as a part is improved.