When a seismic signal propagates through a realistic medium in the Earth, in add ition to anisotropy, the layers may show intrinsic viscoelastic behavior. Thus, an accurate description of wave propagation requires a rheology that accounts for the anisotropic and viscoelastic behavior of rocks. On this basis, the pseudo spectral recursive formulae of viscoelastic and azimuthally anisotropic media are derived. Wavefield forward modeling with the pseudo-spectral method was car ried out in viscoelastic and azimuthally anisotropic media. The numerical results from the pseudo-spectral method clearly show that seismic wavefield is closely related with the viscoelasticity and the azimuth of the principal axes of anis otropy.