In laser thermal stress cleaving of brittle materials using controlled fracture technique,the applied laser energy absorbed in a local area produces a tensile thermal stress that causes the material to separate along the moving direction of the laser beam. The material separation is similar to a crack extension and the fracture growth is controllable. A three-dimensional finite element thermoelastic calculational model with the heat transfer theory is established to investigate the process when pulsed laser is applied to cut the Al2O3 ceramic plate. The temperature field and thermal stress field at the area irradiated by the laser are simulated. During the laser pulse,the distribution of the tensile stress and compressive stress with depth is obtained. The mechanism of crack propagation is investigated by analyzing the development of the thermal stress field during the process.