Abstract: The magnetic torque is the main execution part of a satellite. This paper presents a design of the magnetic torque based on its strength and reliability, which is optimized in dimension by the method of materials mechanics and the finite element calculation to reduce the maximum stress. The results show that the thermal stress is caused by its non-uniform temperature field. The main dangerous positions of the magnetic torque are in the contact interface between the bolt and the support base and the optimization reduces the stress in the critical point.