The applied laser energy absorbed in a local area in laser thermal stress cleaving of brittle materials using a controlled fracture technique produces tensile thermal stress that causes the material to separate along the moving direction of the laser beam. The material separation is similar to crack extension, but the fracture growth is controllable. Using heat transfer theory, we establish a three-dimensional (3D) mathematical thermoelastic calculational model containing a pre-existing crack for a two-point pulsed Nd:YAG laser cleaving silicon wafer. The temperature field and thermal stress field in the silicon wafer are obtained by using the finite element method (FEM). The distribution of the tensile stress and changes in stress intensity factor around the crack tip are analyzed during the pulse duration. Meanwhile, the mechanism of crack propagation is investigated by analyzing the development of the thermal stress field during the cleaving process.