Nonlinear transient analysis is executed to obtain the temperature distribution, and to evaluate the thermal stress of brake drum by using FEA(finite element analysis). The result induces the reason why hair crack and the cause of drum failure occurs and the way how stress of drum decreases. The temperature of drum is in proportion to the drum thickness and it processes nonlinear changes at every points of drum. The higher bulk temperature raises, the more stress difference between inner surface and outer surface makes and the highest bulk temperature is at the corner section. It is necessary for the diminishment of the drum stress to make air flow, between drum and rim, move lively and use the materials of higher conductivity. The hair crack and the cause of drum failure seem to be started at the near corner section.