Simulation of elastic wave propagation has important applications in many areas such as inverse problem and geophysical exploration. In this paper, stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated. They can be expressed explicitly by elasticity constants which are easy to be applied in computations. The 3-D wave simulation for two typical anisotropic media, transversely isotropic media and orthorhombic media, are carried out. The results demonstrate some satisfactory behaviors of the pseudospectral method.