A mathematical model has been developed for the prediction of elastic moduli of three-phase fiber-reinforced composite. This model considers composite materials consisting of three phases, namely, fiber, interphase and matrix, and incorporates the effect of fiber packing. In the present paper, the interphase is assumed to be a homogeneous and isotropic material. The elastic moduli E 11, E22, G12 and G23 have been evaluated and damping coefficients η11, η22, η12 and η23 have been predicted by application of a correspondence principle using this developed model. The effect of interphase volume fraction on loss factors has been evaluated. Prediction of elastic moduli and loss factors has been carried out with a weak and a strong interphase. The calculated results show that the interphase volume fraction and its properties have a very significant effect on loss factor of fiber-reinforced polymer composite. Evaluation of material properties based on the finite element method is presented using representative volume element approach. Results using the developed model are in good agreement with those obtained by FEM and other methods. © Koninklijke Brill NV, Leiden, 2010.