Abstract: In this paper, the expressions of phase velocities for homogeneous and inhomogeneous P, SV, SH plane waves are derived from Christoffel equation. Phase attenuation coefficient and group attenuation coefficient for inhomogeneous and homogeneous plane wave are derived by the method used for extreme anisotropic medium. The relation between phase attenuation coefficient, group attenuation coefficient and azimuth of cracks is studied through numerical calculation. It is concluded that fracture can be indicative by SH wave phase velocity and attenuation coefficient in a homogeneous medium. SH wave attenuation coefficient increases with the increase of inhomogeneous angle, and the angle between its axis of symmetry and the symmetry axis of media also increases correspondingly in inhomogeneous medium; attenuation of seismic wave amplitude is more sensitive to variation of the rock’s physical properties than the variation of wave velocity, and it carries more information about petrophysical properties. Therefore, it can be used to probe the azimuth of cracks, crack density, water content and to forecast and prevent from geological disasters in underground engineering.