The present work is devoted to the numerical analysis of magneto-mechanically coupled mesostructures in the framework of the finite element method. Magnetic materials are used in many industrial applications, thus the demand for environmentally friendly magnets with improved efficiency is continuously increasing. To meet this demand, alternative methods and more environmentally friendly chemical compositions need to be investigated in addition to current process routes. The objective in this work is the numerical analysis of magnetic materials based on a continuum mechanical formulation. On the one hand, the focus is on the development of new algorithms for the efficient treatment of open boundary problems in magnetostatics and their numerical implementation. On the other hand, the implementation of the micromagnetic equations in the framework of the finite element method and the validation of this numerical model is forced. After completion of the validation, polycrystalline magnetic microstructures are numerically analyzed.