Permanent magnet (PM) type transverse flux linear motors (TFLMs) are electromagnetic devices, which can develop directly powerful linear motion. These motors have been developed to apply to high power system, such as railway traction, electrodynamics vibrator, free-piston generator, etc. This paper presents an optimum design of a PM-type TFLM to reduce the weight of motor with constraints of thrust and detent force using response surface methodology (RSM) and genetic algorithms (GAs). RSM is well adapted to make analytical model of motor weight with constraints of thrust and detent forces, and enable objective function to be easily created and a great computational time to be saved. Finite element computations have been used for numerical experiments on geometrical design variables in order to determine the coefficients of a second-order analytical model for the RSM. GAs are used as a searching tool for design optimization of TFLM to reduce the weight of motor and improve the motor performance.