We have studied the formation and growth of solid-electrolyte interphase (SEI) for the case of ethylene carbonate (EC), dimethyl carbonate (DMC) and mixtures of these electrolytes using molecular dynamics simulations. We have considered SEI growth on both Li metal surfaces and using a simulation framework that allows us to vary the Li surface density on the anode surface. Using our simulations we have obtained the detailed structure and distribution of different constituents in the SEI as a function of the distance from the anode surfaces. We find that SEI films formed in the presence of EC are rich in Li2CO3 and Li2O, while LiOCH3 is the primary constituent of DMC films. We find that dilithium ethylene dicarbonate, LiEDC, is formed in the presence of EC at low Li surface densities, but it quickly decomposes to inorganic salts during subsequent growth in Li rich environments. The surface films formed in our simulations have a multilayer structure with regions rich in inorganic and organic salts located near the anode surface and the electrolyte interface, respectively, in agreement with depth profiling experiments. Our computed formation potentials 1.0V vs. Li/Li+ is also in excellent accord with experimental measurements. We have also calculated the elastic stiffness of the SEI films; we find that they are significantly stiffer than Li metal, but are somewhat more compliant compared to the graphite anode.