Knowledge of the elastic properties of Li-Si alloys as a function of Li concentration is crucial in the development of reliable deformation and fracture mechanics models for Si anodes in Li-ion batteries. Here, we have studied these properties using first-principles calculations for both amorphous and crystalline phases observed during lithiation of Si anodes. In the case of crystalline alloys, we present the anisotropic elastic tensors as well as the homogenized Young's, shear, and bulk moduli and the Poisson's ratios. We find that while these moduli decrease in an approximately linear manner with increasing Li concentration leading to significant elastic softening (by about one order of magnitude) in both crystalline and amorphous systems, the Poisson's ratios remain in the range of 0.05-0.20 and 0.20-0.30 in the case of crystalline and amorphous systems, respectively. Further, for a given Li concentration, we find that the amorphous structures are elastically somewhat softer than their crystalline counterparts, the difference being more significant (about 30-40%) in Li-poor phases. Our results underscore the importance of including the concentration dependence of elastic constants in the analysis of stress and deformation fields during lithiation and de-lithiation of Si anodes. (C) 2010 Elsevier B.V. All rights reserved.