NanoCrystalline Metals consist of two distinct phases. Crystalline phase i.e. grains and intercrystalline phase i.e. grain boundaries, triple junctions, and quadruple nodes. Weakening of elasticity in the intercrystalline phase of nanocrystalline metals especially in grain boundaries causes the decrease of the overall elasticity of nanocrystalline metals. Therefore the study of elastic behavior and calculation of elasticity in grain boundaries is important for nanocrystalline metals. The purpose of this research is modeling grain boundaries elasticity in nanocrystalline metals and its calculation. For this purpose, five different metal samples with different crystalline structures are considered and for each of them, three RVEs with different grain size and constant grain boundary thickness is modeled. The behavior of the crystalline phase is considered elastic with cubic symmetry and the behavior of grain boundaries is considered to be elastic. Then the uniaxial tension has been simulated. For the weakening coefficient of grain boundaries the value of 0.76 is obtained by the finite element analysis. To verify the validity of the obtained weakening coefficient. The Young’s modulus of simulated RVEs is compared with the Young’s modulus extracted from MD simulation and experiments in the literature. Keywords: Grain, Grain Boundary, Young’s Modulus, Weakening Coefficient, Bulk Young’s Modulus, Nanocrystal, RVE, Nanocrystalline Metals