Abstract: The general constitutive relationship of transverse isotropy and azimuthal anisotropy,is discussed in this paper. After analyzing the characteristics of elastic waves propagating in these two kids of enisotropic media we deduce generalized expressions of anisotropy parameters which describe the anisotropy degree both in transversely isotropic media and azimuthal anisotropic media. When there is an interface in two anisotropic media the reflection coefficients are discussed respechtiely.The formula derived by Dely et. al. is extended to be used in the symmetric plane in azimuthal anisotropic media. Finally, comparing the exact reflection coefficients formula with Baulk's and Thomsen's approximations for typical shale and gas-sand models and carbonate rock models, we discuss the AVO in the two kinds of anisotropic media and its influence in actual exploration, especially for fraCtured reservoir.