Effects of variations in the elastic and geometrical properties of the constituents of recycled aggregate concrete (RAC) on its elastic constants are investigated. To this aim, a 3D multiscale scheme including Mori-Tanaka homogenization algorithm and finite element method (FEM) is employed. An energy-based homogenization approach is used in FEM to derive the most accurate values from the relationship between the elastic moduli and Poisson’s ratios. The Mori-Tanaka and finite element models are verified with available experimental results. Results indicate that with increasing the elastic modulus of each of the phases of aggregate, old interfacial transition zone (ITZ), old mortar, new ITZ, and new mortar by approximately two times, the elastic modulus and Poisson’s ratio of the RAC vary by 6 and 5%; 0.2 and 0.11%; 24 and 4%; 0.4 and 0.1%; and 52 and 8%, respectively. Furthermore, a change in the thickness of old mortar from 1 to 11 mm reduces the elastic modulus and Poisson’s ratio of the RAC by 24 and 7%, respectively. Altering the aggregate size from 15.9 to 9.9 for 3 mm old mortar thickness and from 13.9 to 9.9 in 5 mm old mortar thickness lead to 14 and 7 percent reduction in elastic modulus.