Transmission line equations are considered for a system consisting of an arbitrary number of electrical conductors. The numerical technique based on finite difference approximation is proposed. First, the original system of differential equations is written in Riemann invariants, and then the resulting equations are approximated according to the finite difference method. In order to obtain the final finite difference scheme with minimal numerical dispersion and dissipation the method of first differential approximation is applied. The novelty lies in obtaining a generalization to the case of an arbitrary number of conductors.