A numerical investigation of anisotropic waves propagating in a magnetized plasma layer is performed. In gyrotropic plasma layers, there are two regions in which electromagnetic waves exist owing to the anisotropic properties of the plasma. Mainly these are Rayleigh pseudosurface waves. In the upper anisotropic region, a wave exists only in a planar waveguide. In the lower anisotropic region, there are two waves. The dispersion and the origin of these waves are analysed. The distribution of the energy and the Poynting vector are unique, and they differ from those of other families of electromagnetic waves. At small wavenumbers, the energy is concentrated in one of the dielectrics and at large wavenumbers, it is concentrated in the plasma.