This paper investigates the saturation mechanism of the nonstationary supercritical mode of parametric wave phase conjugation in a magnetostrictive medium. The numerical simulation considers the two most probable nonlinear mechanisms of interaction between elastic deformation and electromagnetic excitation. For the qualitative study of the dynamics of the system, a one-dimensional numerical simulation is sufficient if applied to an infinite medium with a finite active zone. The temporal form of the conjugate wave is obtained for both hypotheses. Comparison with experiments shows that only one mechanism corresponds to the experimental behavior.