The basic formula of pseudo-spectral method are derived for simulating inhomogeneous anisotropic elastic waves field.The boundary modifying equations of characteristic variables method are derived thoroughly which have been presented by previous authors separately, and the explicit formula of 3D and 2D problems of solid and liquid media are given.2.5D elasticwave field of two models are simulated,moreover, the polarization and time delay of S wave splitting are discussed in detail.