The realistic microstructure of the concrete has been reconstructed using X-ray tomography images and numerically simulated to obtain the effective elastic properties. The concrete under consideration was made of 5 mm coarse aggregate and cement (includes three phases cement, aggregates and macro-pores). 3D reconstructed image of the concrete cube specimen of size 40 mm3 were converted to the finite element mesh. Also, five smaller cubical regions of size two times of coarse aggregate had been cropped to establish a statistical representative volume element (RVE) for concrete. Asymptotic homogenization technique along with periodic boundary conditions was used to obtain the elastic stiffness coefficients. Elastic stiffness matrices were obtained along with associated uncertainties for each case of RVE’s. The obtained stiffness matrices for all cases were fully populated. However the shear-extension and shear-shear coupling were very small as compared to extension – extension, hence can be neglected. The cubical symmetry was observed for all cases as expected for concrete and mean values of engineering constants were closer to the isotropic case, as anisotropy ratios are nearly 1. Hence the concrete can be considered as isotropic with effective values of E= 34 GPa and µ=0.2 (Young’s modulus and Poison’ ratio respectively). The investigation also revealed that a smaller RVE can be considered for the concrete provided the scatter in the properties should be minimum. Later the effect of cement damage was also studied by modelling the damage initiation and propagation using damage-plasticity model for cement stiffness degradation. The strength of the concrete in tension and shear is obtained as 3.72 and 1.65 MPa respectively.