Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive imaging modality for generating electrical conductivity images of biological tissues with high spatial resolution. In this paper, we create a numerical model, including a permanent magnet, a coil, and a two-layer coaxial cylinder with anisotropic electrical conductivities, for the MAT-MI forward problem. We analyze the MAT-MI sources in two cases, on a thin conductive boundary layer and in a homogeneous medium, and then develop a feasible numerical approach to solve the MAT-MI sound source densities in the anisotropic conductive model based on finite element analysis of electromagnetic field. Using the numerical finite element method, we then investigate the magnetoacoustic effect of anisotropic conductivity under the inhomogeneous static magnetic field and inhomogeneous magnetic field, quantitatively compute the boundary source densities in the conductive model, and calculate the sound pressure. The anisotropic conductivity contributes to the distribution of the eddy current density, Lorentz force density, and acoustic signal. The proposed models and approaches provide a more realistic simulation environment for MAT-MI.