Abstract: Based on the Christoffel equation， the Christoffel equation of EDA (extensive dilatancy anisotropy) medium is derived by Bond transformation. The exact formulas for 3-D phase velocity, group velocity and polarization vector are derived from the nonzero solutions of the Christoffel equation. The influences of polar and azimuth of symmetry axis of HTI (horizontal transverse isotropy) and EDA media on phase velocity, group velocity and polarization vector are studied through numerical calculation and the results are displayed by 3D graph using Matlab, which makes the results more colorful and intuitive. By setting the polar and azimuth to zero, the phase velocity, group velocity of HTI and VTI (vertical transverse isotropy) media are derived, the 3D phase velocity, group velocity of EDA media are verified by degeneration. The result proves that it is possible to explore the azimuth of cracks, crack density, the occurrence of hazard body by azimuth seismic exploration.