This thesis investigates a potential imaging method to provide high spatial resolution impedance information, known as Magneto-Acousto-Electrical Tomography (MAET). Both the forward and the inverse problems in MAET are explored by theoretical analysis and numerical simulations. The current density distribution that would exist in a sample if a current were to be applied through the measurement electrodes or a coil is first mapped by applying the reciprocity theorem of electromagnetism. Once the current distribution is known, it is possible to calculate the conductivity from this current density by solving a system of ordinary differential equations for the conductivity. These are obtained by applying the method of characteristics on the relevant Maxwell's equations involving the conductivity.