Elastic constants of single-crystal Au 5 Sn and AuSn were determined through ab initio calculations to characterize their polycrystalline elastic behavior and elastic anisotropy. The ideal bulk (K = 127 GPa), shear (G = 28 GPa), and YoungÕs modulus (E = 78 GPa), as well as PoissonÕs ratio (v = 0.398), of Au 5 Sn were determined using the Voigt-Reuss-Hill method and were very close to the range of experimental results; the values of AuSn were 88 GPa, 15 GPa, 42 GPa, and 0.420, but its ideal YoungÕs modulus was much smaller than the experimentally obtained values. This unusual discrepancy in the YoungÕs modulus of AuSn is probably attributed to its extraordinarily high anisotropy in YoungÕs modulus, with a 95 GPa difference between its maximum and minimum values. Au 5 Sn exhibits relatively low anisotropy in YoungÕs modulus with a maximum-minimum difference of 38 GPa.