So far, Permanent Magnet (PM) clutches have been broadly used as torque transmission devices. With the aim of effective utilization of materials and energy in the manufacturing of PM clutches, design optimization has been widely applied. Generally, PM clutches are optimized applying linear dimensions as optimization parameters. On the contrary, optimization of PM clutch shapes has not been done extensively. Therefore, this paper performs optimization of PM 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 %. Although the obtained shapes appear to be highly intricate, it does not pose an obstacle for modern manufacturing techniques.