This dissertation describes the development and testing of modified embedded atom method (MEAM) interatomic potentials for Al, Si, Mg, Cu, Fe, and their alloys, with primary concentration on Mg-Al system. We performed the density functional theory (DFT) based ab initio calculations to determine the structural and elastic properties of element pairs that are impractical to obtain from experimental measurements. Specifically, we estimated the cohesive energy, equilibrium atomic volume, bulk modulus, and elastic moduli of every element pair in the NaCl reference structure. Based on the results of DFT calculations, MEAM parameters for each element pair were constructed. We extensively tested the new MEAM potential for Mg-Al alloy system. The new Mg-Al MEAM potential was compared with DFT calculations, previously published semi-empirical interatomic potentials, and experiments. Applicability of the new MEAM potential to atomistic modeling was demonstrated by calculating stress-strain responses from molecular dynamics (MD) simulations of Mg and Al systems in a variety of configurations. The effects of alloying, porosity, and strain rate conditions on the stress-strain response were quantified. The underlying mechanisms for tension-compression asymmetry observed in the macroscale experiments of Mg alloys were investigated at the nanoscale. This work presents a contribution to the task of bridging quantum-mechanical and classical atomistic scale simulations. Information from ab initio electronic structure calculations was used to construct parameters of semi-empirical MEAM potentials for large-scale atomistic simulations of alloys. The results of the new MEAM models compare extremely well to those from other published interatomic potentials. The applicability of the new MEAM potential to investigate nanoscale mechanisms of the deformation and fracture for Al, Mg and Mg-Al alloys was demonstrated. It has been shown that the MEAM provides a single universal formalism for classical atomistic simulations of a wide range of elements and their alloys.