Experimental and theoretical research showed that in predicting concrete’s elastic modulus, it should be modelled as a three-phase composite material at a mesoscopic level, consisting of aggregates, interfacial transition zone (ITZ) and cement paste, and that the proportions, mechanical properties and interaction of the three phase constituents should all be considered in the prediction. The present paper attempts to develop a numerical method that can predict the elastic modulus of three-phase concrete made with two different aggregates. In this method, the mesostructure of concrete is simulated and the lattice type model is modified to take into account the mechanical properties of the cement paste, ITZ, and fine and coarse aggregates of concrete. The finite element method is then employed for analyzing the stress and strain in concrete and therefore for determining its elastic modulus. Finally, the developed numerical method is verified by comparison with the experimental results obtained from the research literature. The paper concludes that the numerical method can predict with reasonable accuracy the elastic modulus of concrete made with two different aggregates.