Abstract:Based on the propagation theories of seismic waves in the anisotropic medium and in the cracked two-phase medium separately, the constitutive relations and dynamic equations of the propagation of seismic waves in cracked two-phase anisotropic medium with symmetric axis of 4 rank have been derived. It was pointed that 6 types of quasi-longitudinal and quasi-shear waves may propagate in the cracked two-phase anisotropic medium. They are:QP1(quick longitudinal wave), QP2(slow longitudinal wave), QSV1,QSH1(two splitting quick shear waves) and QSV2,QSH2(two splitting slow shear waves). As an example, the propagation of plane waves was analyzed further.