The self-consistent effective field method of solution of the homogenization problem for matrix composite materials is considered. The principal hypothesis of the method concerns the local exciting fields acting on the inclusions. This field is assumed to be constant and the same for all the inclusions (quasi-crystalline approximation). In addition to the shapes, volume fraction and properties of the inclusions, the method requires information about the shape of correlation hole for a typical inclusion in the composite. It is shown that the effective conductive and elastic properties of the composites depends strongly on the correlation hole aspect ratios. The method is applied to solutions of the homogenization problem for composites with random and regular set of ellipsoidal inclusions. The predictions of the method are compared with experimental data and results of numerical simulations. Well-known Mori-Tanaka method coincides with the effective field method by the additional assumption that the aspects of the correlation hole coincide with the aspect ratios of the ellipsoidal inclusions. It is shown that the considered version of the method can violate symmetry of effective conductivity and elastic stiffness tensors of the composite when it is applied to composites with several different families of the inclusions.