Two models of hysteresis including the influence of an elastic stress on the magnetic behavior of the material are analyzed. They are shown to have different properties, but comparable accuracy. The Preisach model needs a large amount of experimental data, but is very general, whereas the internal variable model uses few parameters, but can not fit any shape of hysteresis loops. The advantages and drawbacks of the two approaches are illustrated in the case of two electrical steels: a 0.5 mm thick Fe-3%Si alloy and a 0.4 mm thick Fe48%-Co48%-Va2% alloy.