Finally cut surface obtained to provide a method for cutting a machining target material without largely deviated from the planned cutting planes. After the laser beam to cut surface of the processing target material is absorbed to form a modified region, a method for cutting a machining target material is cut along a processing target material to cut surface, Law of cut surface line, without the normal to the predetermined angle in a predetermined low index plane of the processing target material, as the distance crack distance of irradiation line between the laser beam along a predetermined low index plane is not extended, form a plurality of lines of the cracking suppressing processing step of forming side by side modified region, between the modified area is formed line-shaped at crack suppression processing step, the modified regions of the additional linear, irradiation of the adjacent laser beam cracking along the distance between the lines in a predetermined low-index plane is to contain, and cracking promotion processing step of forming a distance that extension.