In this paper, we study a more general method for obtaining elastic parameters for materials with small elliptical holes. Using the examples of a circular hole and a crack, it is shown that these special cases are obtained from the derived more general solution. Two methods are used in the work: Taylor and self-consistency. In the first one, the interaction between the holes is neglected, while in the second one, the "weak interaction" so wound is used. The paper shows that both methods for a small concentration of holes give satisfactory results.