This paper presents magnet shape optimization of permanent magnet coupling (PMC) for a 50 hp chemical pump system considering the linear and non-linear design parameters. Firstly, the size and topology of PMC are considered for the initial model. PM eddy currents are analyzed to select the initial model. Secondly, an optimization process is performed to get the maximum pullout torque for a given PM volume. The optimization is based on a two step process; firstly, non-linear design parameters are considered for optimization using 2-D finite element method (FEM). The optimization is performed to maximize the pullout torque of the PMC and reducing the PM volume. Kriging method and genetic algorithm are utilized due to the non-linearity of the design parameters in the optimization process. Secondly, linear design parameters are adjusted and 3-D FEM is utilized to achieve the target and incorporate the end effects. Using two-step design process, the number of design parameters are reduced in the first step which simplify the optimization process and computational time is reduced using 2-D FEM. After that, the axial length of the PMC can be used as a linear design parameter to obtain the required pull-out torque. The optimized model is then simulated using 3-D FEM to incorporate the end effects and experimental results are then presented.