Abstract: In this talk, a coupled atomistic and continuum model for numerical simulations of dynamics of crystalline solids will be presented. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achieved based on a general framework for multiscale modeling - the heterogeneous multiscale method (HMM). An explicit coupling condition at the atomistic/continuum interface is derived. Application to the dynamics of brittle cracks will be presented.