The hypotheses of the effective medium method (EMM) and its modifications (Kerner’s method, differential effective medium method) are formulated. The method and its modifications are applied to the solution of the homogenization problem for conductive and elastic matrix composite materials with ellipsoidal inclusions. Predictions of the method are compared with experimental data and results of numerical simulations. The results of the application of the method to the media with elliptical cracks are presented.