The thesis deals with finite element method simulations of the two-degree of freedom spherical induction actuator performed using the 2D and 3D models. In some cases non-linear magnetization curves, rotor movement and existence of higher harmonics are taken into account. The evolution of the model leading to its simplification is presented. Several rotor structures are tested, namely the one-layer, two-layers and two-layers-with-teeth rotor. The study of some rotor parameters, i.e. teeth number and size, external and internal layer thickness, in order to improve the actuator electromechanical conversion and reduce the torque ripple is performed. The influence of the rotor teeth geometrical form on the electromechanical conversion is shown. General actuator parameters such as the airgap, source current and parameters of the magnetic material are verified as well. Finally the superiority of the two-layers-with-teeth rotor structure over the one-layer and two-layers structures is confirmed.