The laser cleaving process is a new method to cut brittle materials such as glass, silicon and ceramics. In this dry process, the material is diced only by the thermal stress induced by the laser irradiation. Therefore, the material is not contaminated with the coolant generally used in the mechanical dicing process, but teh thermal damages are caused on the irradiated surface. The objective of this paper is the prevention of thermal damages in the laser cleaving process of silicon wafer. The cleavin experiments are conducted with pulsed ND:YAG laser and cw Nd:YAG laser. In the cleaving with pulsed laser, the temperature required for crack propagation is investigated by measuring with a two-color pyrometer developed. The critical temperature at which the stress intensity factor slightly exceeds the fracture toughness depends on the pulse frequency, the pulse width, the scanning velocity of laser spot and the material properties. The temperature is also confirmed by the thermal stress analysis. And then, for the cleaving with cd laser, a refrigerating-chuck system is developed to reduce the thermal damage of workpiece. The system refrigerates the working table below the freezing point of water, and the material is fixed on the table by the frozen water between the material and the table. While the silicon oxide is caused on the surface of wafer in the room temperature, the refrigerating-chuch can prevent the thermal damage and improve the linearity of the cleaving trajectory and the reliability of the cleaving process.