Provided is a method which can stably cut a substrate while reducing a bending moment (break pressure) required for the cutting. The method for cutting a fragile material substrate includes: a step for forming a crack along a planned cut line; and a break step for separating the substrate along the formed crack by applying a bending moment. The step for forming the crack forms a cyclic crack having the maximum depth limited by a clamping stress region inside the substrate while the crack depth is changed along the planned cut line by a cycle of the heating condition or/and the cooling condition by cyclically changing the heating condition and/or the cooling condition along the planned cut line. In the break step, a bending moment is applied from the rear surface side of the substrate to the cyclic crack.