This paper proposes an optimal rotor design method of an interior permanent magnet synchronous motor (IPMSM) by using a permanent magnet (PM) shape. An IPMSM is a structure in which PMs are buried in an inner rotor. The torque, torque ripple, and safety factor of IPMSM can vary depending on the position of the inserted PMs. To determine the optimal design variables according to the placement of the inserted PMs, parameter analysis was performed. Therefore, a response surface methodology, which is one of the statistical analysis design methods, was used. Among many other response surface methodologies, Box-Behnken design is the most commonly used. For the purpose of this research, Box-Behnken design was used to find the design parameter that can achieve minimum experimental variables of objective function. This paper determines the insert position of the PM to obtain high-torque, low-torque ripple by using a finite-element-method, and this paper obtains an optimal design by using a mechanical stiffness method in which a safety factor is considered.Index Terms-Box-Behnken design, finite-element-method (FEM), optimal design, permanent magnet (PM), safety factor, synchronous motor.