Numerical models of the micromagnetic structure of titanomagnetite particles require the consideration of magnetostriction. A new technique for calculating magnetostrictive self energies in finite element models is introduced. The method is based on the continuum theory of defects [Kr¿ner, 1958>. By solving the biharmonic equation for the second order stress function tensor in an infinite elastically homogeneous medium the treatment of the magnetostrictive energy becomes similar to the treatment of demagnetizing energy. Fast Fourier Transformation can therefore be applied to the calculation of both, demagnetizing and magnetostrictive energies. ¿ American Geophysical Union 1996