A method of cutting a semiconductor material substrate, a piezoelectric material substrate or a glass substrate, comprising steps of: irradiating the substrate with a laser light, characterized in that the laser light has a pulsed laser light having a pulse width not larger than 1μs at a converging point within the substrate, so that the converging point of the pulsed laser light is positioned within the substrate and a peak power of the laser light at the converging point is not smaller than 1 X 10 8 (W/cm 2); and further characterized by the following steps: moving the converging point of the pulsed laser light with respect to the substrate relatively along a line along which the substrate is intended to be cut sequentially to form, at respective converging points of the pulsed laser light, a plurality of modified spots, wherein at least one of the magnitude of speed of the moving converging point of the pulsed laser light with respect to the substrate and the magnitude of repetition frequencey of the pulsed laser light is controlled such that each modified spot overlaps both of the adjacent modified spots formed along the line along which the substrate is intended to be cut, so as to make a continuous modified region functioning as a starting point for cutting the substrate by the plurality of the modified spots only within the substrate without melting a pulsed laser light incident surface of the substrate along the line along which the substrate is intended to be cut; further wherein the modified spot is a crack spot and the modified region is a crack region when the substrate is a glass substrate or piezoelectric material substrate, or the modified spot is a molten processed spot and the modified region is a molten processed region when the substrate is a semiconductor material substrate, or the modified spot is a refractive index change spot and the modified region is a refractive index change region caused by a permanent structural change such as ionic valence change, crystallization or polarization orientation when the substrate is a glass substrate and the laser light pulse width is Ins or less, further wherein the starting point formed in the substrate is formed only by the laser irradiation converging within the substrate, and a crack is generated from the modified region functioning as the starting point for cutting and grown from the starting point and the crack reaches to a front and back surface of the substrate so that the substrate is to be cut, and; cutting the substrate along the line along which the substrate is intended to be cut. irradiating the substrate with a laser light, characterized in that the laser light has a pulsed laser light having a pulse width not larger than 1μs at a converging point within the substrate, so that the converging point of the pulsed laser light is positioned within the substrate and a peak power of the laser light at the converging point is not smaller than 1 X 10 8 (W/cm 2); and further characterized by the following steps: moving the converging point of the pulsed laser light with respect to the substrate relatively along a line along which the substrate is intended to be cut sequentially to form, at respective converging points of the pulsed laser light, a plurality of modified spots, wherein at least one of the magnitude of speed of the moving converging point of the pulsed laser light with respect to the substrate and the magnitude of repetition frequencey of the pulsed laser light is controlled such that each modified spot overlaps both of the adjacent modified spots formed along the line along which the substrate is intended to be cut, so as to make a continuous modified region functioning as a starting point for cutting the substrate by the plurality of the modified spots only within the substrate without melting a pulsed laser light incident surface of the substrate along the line along which the substrate is intended to be cut; further wherein the modified spot is a crack spot and the modified region is a crack region when the substrate is a glass substrate or piezoelectric material substrate, or the modified spot is a molten processed spot and the modified region is a molten processed region when the substrate is a semiconductor material substrate, or the modified spot is a refractive index change spot and the modified region is a refractive index change region caused by a permanent structural change such as ionic valence change, crystallization or polarization orientation when the substrate is a glass substrate and the laser light pulse width is Ins or less, further wherein the starting point formed in the substrate is formed only by the laser irradiation converging within the substrate, and a crack is generated from the modified region functioning as the starting point for cutting and grown from the starting point and the crack reaches to a front and back surface of the substrate so that the substrate is to be cut, and; cutting the substrate along the line along which the substrate is intended to be cut.