The time-dependent system of partial differential equations of the
 second order describing the electric wave propagation in
 electrically and magnetically anisotropic homogeneous media is
 considered in the paper. A method for the computation of the polynomial solutions of the initial value problem for the considered system is proposed.
 Symbolic computations are used and these symbolic computations are implemented in Maple. It is proved also that these polynomial solutions are approximate solutions of the considered initial value problem with smooth initial data and the inhomogeneous term. The computational experiments confirm the robustness of the suggested method for the computation of electric fields in general electrically and magnetically anisotropic media.