An analytical model is developed to assess the elastic-plastic dynamic response of fully backed sandwich plates under localized impulse load. The core is modeled as an elastic-perfectly plastic foundation. The top face sheet is treated as an individual plate resting on the foundation. The elastic-plastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique. The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed. The model can be used to predict the impulse-induced local effect on fully backed sandwich plates.