The dynamics of magneto-elastic materials is described by a nonlinear parabolic hyperbolic system which couples the equations of the magnetization and the displacements. We propose a model for the two-dimensional case and establish the existence of weak solutions. Our starting point is the Gilbert-Landau-Lifshitz equation introduced
for describing the dynamics of micromagnetic processes. Three terms of the total free energy are taken into account: the exchange energy, the elastic energy and the magneto-elastic energy usually adopted for cubic crystals, neglecting, in this approach, the contributions due to the anisotropy and the demagnetization effects.
The analysis of the equations is carried out in 2D framework which allows us further simplificative hypotheses mainly concerning the assumption of small plane displacements. The existence theorem for the proposed differential system is proved combining the Faedo-Galerkin approximation with the penalty method which introduces a small parameter. The convergence as the parameter vanishes is deduced from compactness properties.