The paper presents the results of FEM 2D computational studies of a three-phase Direct Current Excited Flux Switching Machine (DCEFSM) electric motor with rotor teeth and stator teeth. The aim of the research was to minimize the cogging torque of the machine by changing the geometry of the rotor teeth and the size of the air gap between the stator and the rotor, with the operating torques unchanged. Computational studies were carried out on the influence of the width of the rotor teeth, the radius of the rounding of their corners, and the size of the air gap on the cogging torque and machine operating torques. The results of the calculations made it possible to select the dimensions of the rotor and the air gap in such a way that the maximum cogging torque was reduced more than six-fold, with the machine operating torques being unchanged. The calculations also showed that it is not possible to increase the value of the operational torques by further changes in the geometry of the rotor teeth and the size of the air gap of the machine.