Nano-sized ferromagnetic particles may play an important role in changing or improving mechanical performance of a smart material that is composed of a matrix and the ferromagnetic particles. When subjected to a magnetic field, the material changes in shape or dimension, which process is called magnetostriction. Since magnetostriction is a multi-physics phenomenon, it is inevitable that we should adopt a numerical framework to solve such a nonlinearly coupled problem. In the present study, the construction of a numerical framework for the material, for which elastic and magnetic properties are coupled to each other, is illustrated.