We have studied the elastic properties of Li–Sn alloys as a function of Li concentration using first principle calculations. Here, we present the anisotropic elastic tensors as well as the orientation-averaged bulk, Young's and shear moduli and the Poisson's ratios for crystalline alloys. Our results demonstrate that crystal anisotropy has a significant effect on the stiffness of the material. We suggest that the bulk, shear and Young's moduli of isotropic Li x Sn alloys decrease monotonically with increasing Li concentration, resulting in elastic softening. On the other hand, highly anisotropic structures of very similar Li contents deviate from linearity indicating either elastic hardening or softening of the material. In addition to the significant role of anisotropy, our results also underscore the importance of including the concentration dependence of the elastic constants in the analysis of deformation during lithiation/delithiation of Sn anodes.