Abstract: In this talk we present a concurrent atomistic-continuum (CAC) method for modeling and simulation of transport processes in crystalline materials. The CAC formulation extends the Irving-Kirkwood procedure for deriving transport equations and fluxes for homogenized molecular systems to that for polyatomic crystalline materials by employing a concurrent two- level structural description of crystals. A multiscale representation of conservation laws is formulated that holds instantaneously, as a direct consequence of Newton’s second law, using the mathematical theory of generalized functions. Finite element (FE) solutions to the conservation equations, as well as fluxes and temperature in the FE representation, are introduced, followed by numerical examples of atomic-scale structures of interfaces, dynamics of fracture and dislocations, and phonon transport in multiscale structured materials. In addition to providing a methodology for concurrent multiscale simulation of transport processes under a single theoretical framework, the CAC formulation can also be used to compute fluxes (stress and heat flux) in atomistic and coarse-grained atomistic simulations.