PURPOSE: To facilitate cutting of a brittle material plate along a desired curve without chipping and to make the cut surface smooth in the subject cutting process of the plate.

CONSTITUTION: In a cutting method by making a partial cut (3) in the outer peripheral part of a plate (W) made of a brittle material, subsequently moving a cutting-heater along a prescribed cutting line (L) starting from the above- mentioned partial cut (3) and advancing cutting of the plate from the above- mentioned partial cut (3) as the starting point, the part of the above-mentioned plate (W) along the above-mentioned cutting line (L) is preheated. A fine cut is preliminarily made along the above-mentioned prescribed cutting line (L) on the surface of the above-mentioned plate (W).