Summary: The coupling between two distinct numerical methods presents a major challenge, especially in the case of discrete-continuum coupling for dynamic simulations. This paper presents a general multiscale framework for coupling the discrete element method (DEM) and the finite difference method (FDM). DEM has been shown to be particular suitable for capturing physical phenomena at small length scales where continuum mechanics description no longer applies. Its efficiency, however, is limited because of the computational power required. A multidomain analysis coupling DEM and FDM is thus proposed to reduce the computational cost. To couple overlapping DEM and FDM, a bridging scale term is introduced such that compatibility of dynamic behavior between the DEM-based and the FDM-based models is enforced. This multiscale method couples two commercial packages: the DEM-based code, particle flow code, and the FDM-based code, fast lagrangian analysis of continua. The new method is applied to several reference dynamic tests. Results using the proposed method compare well with benchmark simulations from FDM and DEM.