Many imaging techniques are playing an increasingly significant role in clinical diagnosis. In the last years especially noninvasive electrical conductivity imaging methods have been investigated. Magnetoacoustic tomography with magnetic induction (MAT-MI) combines favourable contrast of electromagnetic tomography with good spatial resolution of sonography. In this paper a finite element model of MAT-MI forward problem has been presented. The reconstruction of the Lorentz force distribution has been performed with the help of a time reversal algorithm.