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The Cu-Sn alloys have been used since ancient times. At present they attract much interest since the formation and growth of Cu-Sn intermetallic compounds, namely, Cu3Sn and Cu6Sn5, play an important role in the kinetics of the soldering reaction in microelectronics packaging. Their formation kinetics as well as mechanical properties has shown to be crucial for the integrity of solder joints. In this work, we report elastic properties of Cu3Sn and Cu6Sn5 crystalline phases using first-principles calculations based on the density functional theory. The elastic anisotropy of these phases, which is difficult to resolve from experiments, is fully discussed. Our results show that both crystalline phases have the greatest stiffness along the c direction. In particular, Cu3Sn exhibits in-plane anisotropy, which is associated with the lattice modulation within the superstructure. We also propose a void formation mechanism based on the computed bond anisotropy of Sn-Cu and Cu-Cu in Cu3Sn.