To obtain a better understanding on the failure mechanism of lithium ion batteries during charging-discharging, we have systematically studied the mechanical properties of Li−Sn alloys based on the density functional theory, including elastic constants such as the orientation-averaged bulk, shear and Young’s moduli and Poisson’s ratios, as well as the anisotropy and brittleness-ductility. It is shown that bulk, shear and Young’s moduli of isotropic LixSn alloys decrease almost linearly with the increase of Li concentration. Further, based on the analysis of shear to bulk modulus and Poisson’s ratios, it is inferred that Li−Sn alloys are brittle. The poor cycle performance and crushing failure of Sn anode materials during charging and discharging are mainly due to a transition of electrode material properties from ductility to brittleness.