Abstract: In this paper, the equation of anti-plane wave motion in a two-dimensional finite element model is first separated into two one-dimensional simultaneous equations by-means of the separating variable method, analytical solutions of the above equations are ob-tained. According to the solutions, various aspects of the wave propagation in the discrete model is finally systematically studied: dispersion, cut-off frequency, parasitic oscillation and appendent anisotropic properties of wave propagation. In additio...