The method of electrodynamic averaging is described, by which one can obtain the effective dielectric permittivity of volume anisotropic structure determined by the shape of particles, their geometrical sizes, electromagnetic parameters and spatial dense media, to consider multiple interactions between scattering elements and dispersion properties of the media. Tensors of the dielectric permittivity of anisotropic structures are given as the dielectric permittivity of media which sizes and electromagnetic parameters are fluctuating near the average values. The known formulae of dielectric mixing theory are derived from the obtained results in a numbers of cases.