In this paper, a possible applicability of artificial neural networks to predict the elastic modulus of composites with ellipsoidal inclusions is investigated. Besides it, based on the general micromechanical unit cell approach, theoretical formula is also developed, for effective elastic modulus of composites containing randomly dispersed ellipsoidal in homogeneities. Developed theoretical model considers the ellipsoidal particles to be arranged in a three-dimensional cubic array. The arrangement has been divided into unit cells, each of which contains an ellipsoid. Practically in real composite systems neither isostress is there, nor isostrain, and besides it due to the effect of random packing of the phases, non-uniform shape of the particles, we are forced to include an empirical correction factor. We are forced to include an empirical correction factor in place of volume fraction which provided a modified expression for effective elastic modulus. Empirical correction factor is correlated in terms of the ratio of elastic moduli and the volume fractions of the constituents. Numerical simulations has also been done using artificial neural network and compared with the results of Halpin-Tsai and Mori-Tanaka models as well as with experimental results as cited in the literature. Calculation has been done for the samples of Glass fiber/nylon 6 composite (MMW nylon 6/glass fiber), Organically modified montmorillonite (MMT)/High molecular weight (HMW) nylon 6 nanocomposite ((HE)₂M₁R₁-HMW nylon 6), Epoxy-alumina composites and MXD6- clay nanocomposite. It is found that both the theoretical predictions by the proposed model and ANN results are in close agreement with the experimental results.