To achieve high speed cutting in full-body thermal-stress cutting of a brittle material where the upper limit of the speed is the stress propagation speed.

The full-body thermal-stress cutting of a brittle material 2 is conducted by separating into two processes of thermal-stress generation and crack spreading. The thermal-stress generation is made by concentrating irradiated laser beams 8 onto a concentration point 10 of a glass plate 2 with a concentration lens 9 and scanning linearly in the scanning direction 3. The crack spreading starts at an initial crack 12, proceeds along the laser scanning line in the reverse direction 11 opposite to the scanning direction 3 of the irradiated laser beams 8 and reaches the start point of laser irradiation. Since the thermal-stress cutting of the brittle material is separated into two processes of generation of thermal-stress distribution and crack spreading, the upper limit of which is the stress propagation speed, speed-up of both processes can be achieved each under independent conditions thereby overall speed-up of thermal-stress cutting phenomenon can be achieved.