The most rigorous effective medium approximations for elastic moduli are elaborated for matrix composites made from an isotropic continuous matrix and isotropic inclusions associated with simple shapes such as circles or spheres. In this paper, we focus specially on the effective elastic moduli of the heterogeneous composites with arbitrary inclusion shapes. The main idea of this paper is to replace those inhomogeneities by simple equivalent circular (spherical) isotropic inclusions with modified elastic moduli. Available simple approximations for the equivalent circular (spherical) inclusion media then can be used to estimate the effective properties of the original medium. The data driven technique is employed to estimate the properties of equivalent inclusions and the Extended Finite Element Method is introduced to modeling complex inclusion shapes. Robustness of the proposed approach is demonstrated through numerical examples with arbitrary inclusion shapes. Keywords: data driven approach; equivalent inclusion, effective elastic moduli; heterogeneous media; artificial neural network.