AbstractAn effective medium approach (CPA) for calculating the static wave‐number‐dependent effective dielectric function of strongly heterogeneous composites with randomly oriented anisotropic components is presented, where the composite is supposed to consist of a random arrangement of homogeneous regions (grains) with known material properties. Final formulae governing the effective dielectric function at arbitrary wave numbers are given for spherical and cylindrical grain shapes. In the long‐wavelength limit the general case of ellipsoidal shape is considered and a marked dependence of the effective permittivity on the eccentricity is obtained for moderate and large aniso