We investigated the elastic properties of two tin-copper crystalline phases, the η′-Cu6Sn5 and ε-Cu3Sn, which are often encountered in microelectronic packaging applications. The full elastic stiffness of both phases is determined based on strain-energy relations using first-principles calculations. The computed results show the elastic anisotropy of both phases that cannot be resolved from experiments. Our results, suggesting both phases have the greatest stiffness along the c direction, particularly showed the unique in-plane elastic anisotropy associated with the lattice modulation of the Cu3Sn superstructure. The polycrystalline moduli obtained using the Voigt-Reuss scheme are 125.98 GPa for Cu6Sn5 and 134.16 GPa for Cu3Sn. Our data analysis indicates that the smaller elastic moduli of Cu6Sn5 are attributed to the direct Sn–Sn bond in Cu6Sn5. We reassert the elastic modulus and hardness of both phases using the nanoindentation experiment for our calculation benchmark. Interestingly, the computed polycrystalline elastic modulus of Cu6Sn5 seems to be overestimated, whereas that of Cu3Sn falls nicely in the range of reported data. Based on the observations, the elastic modulus of Cu6Sn5 obtained from nanoindentation tests admit the microstructure effect that is absent for Cu3Sn is concluded. Our analysis of electronic structure shows that the intrinsic hardness and elastic modulus of both phases are dominated by electronic structure and atomic lattice structure, respectively.