This paper performs optimization of permanent magnet clutch shapes with the following objectives: maximum tangential attraction force and minimum volume of utilized materials. To form optimal shapes, the points on the clutch surface are chosen as optimization parameters. The optimization is carried out using Ārtap framework in connection with COMSOL software, where the 3D model of the clutch has been created. After the optimization, the tangential attraction force has increased by 13% and the volume of the clutch has been reduced by 24%.