Amethodof cutting a semiconductor material substrate, a piezoelectric material substrate or a glass substrate, comprising steps of: irradiating a substrate with a pulsed laser light, characterised in that the pulsed layer light has a pulse width no larger than 1μs at a converging point within the substrate, sothattheconvergingpoint of the pulsed laser light ispositioned 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) to form a plurality of modified spots within the substrate to form a modified region functioning as a starting point for cutting the substrate, the modified spots being formed along a line along which the substrate is intended to be cut by converging the pulsed laser light at positions closer to a laser light incident surface of the substrate than a center position in a thickness of the substrate; 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 isamoltenprocessed 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 sructural change such as ionic valence change, crystallization or polarization orientation when the substrate is a glass substrate and the laser light pulse width is lns or less, causing a crack which is naturally grown from the modified region on the laser light incident surface of the substrate along the line along which the substrate is intended to be cut; and after the causing, applying a force to the substrate to make the crack further grow to cut the substrate. irradiating a substrate with a pulsed laser light, characterised in that the pulsed layer light has a pulse width no larger than 1μs at a converging point within the substrate, sothattheconvergingpoint of the pulsed laser light ispositioned 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) to form a plurality of modified spots within the substrate to form a modified region functioning as a starting point for cutting the substrate, the modified spots being formed along a line along which the substrate is intended to be cut by converging the pulsed laser light at positions closer to a laser light incident surface of the substrate than a center position in a thickness of the substrate; 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 isamoltenprocessed 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 sructural change such as ionic valence change, crystallization or polarization orientation when the substrate is a glass substrate and the laser light pulse width is lns or less, causing a crack which is naturally grown from the modified region on the laser light incident surface of the substrate along the line along which the substrate is intended to be cut; and after the causing, applying a force to the substrate to make the crack further grow to cut the substrate.