This paper describes the main stages of development of a numerical tool dedicated to the modeling of the magnetoelectric effect. The proposed approaches enable to take into account the nonlinearities of the material, a static and dynamic excitation and a transient state. The developed models are based on the finite element method in 2 or 3 D. To reduce the computation time of frequency-dependent numerical models, the Proper Generalized Decomposition, which is a Model Order Reduction method, is introduced. Each proposed model is illustrated with an application example