The diagram technique for calculation of the dynamic properties of an anisotropic media with randomly distributed inclusions (pores, cracks) is developed. Statistical description of inclusions is determined by distribution function dependent on five groups of parameters: overcoordinates; over angles of orientation of shapes; over angles of orientation of crystallographic axes; over aspect ratio (in a case of ellipsoidal inclusions); over types of phase of inclusions. Such statistical approach allows to take into consideration any type and order of correlation interactions between inclusions. The diagram series for an average Green function is (GF) constructed. The accurate summation of this series leads to a nonlinear dynamic equation for an average GF (Dyson equation). The kernel of this equation is a mass operator which depends on frequency and can be presented in a form of diagram series on accurate GF. The mass operator coincides with effective complex tensor of elasticity (or conductivity) in a local approximation. An expansion of effective dynamic elastic (transport) tensor on distribution functions of any order is obtained. It is shown that correlation between homogeneities can produce an effective elastic and transport parameters anisotropy. In correlation approximation the dispersion dependencies of the effective elastic constants are studied. Frequency dependencies of a coefficient anisotropy of the elastic properties as function of statistical distributed inclusions over coordinates (isotropic matrix and isotropic (spherical) inclusions) are obtained.