In this study, numerical computations are performed to predict the thermal and stress history of sapphire during the cooling process in a Kyropoulos furnace. The thermal distribution during the cooling process is controlled by the power reduction process. During the cooling process, the higher stress is located in the region near the sapphire seed crystal, the crystal center and at the crystal surfaces with large curvature. The results show that as time increases the resultant temperature gradient and the von Mises stress inside the crystal declines. The direction of heat flow at the bottom of the crucible wall changes when the heat supply from the bottom heater in the crucible is less than the heat removal from the crucible support rods. This causes a resultant temperature gradient and sudden increase in the von Mises stress inside the crystal. The highest von Mises stress in the crystal during the whole cooling process appears after this change. The fast cooling process causes a higher value of maximum von Mises stress, but releases the thermal stress more quickly. (C) 2013 Elsevier B.V. All rights reserved.