An analytical model is developed to examine a low impulsive projectile impact on a fully clamped sandwich beams by considering the coupled responses of the core and the face sheets. Firstly, based on the dynamic properties of foam cores, the sandwich beam is modeled as two rigid perfectly-plastic beams connected by rigid perfectly-plastic springs. Different from the previous sandwich beam model, the transverse compression and bending effects of the foam core are considered in the whole deformation process. Based on this model, different coupling mechanism of sandwich beams are constructed so that an analytical solution considering small deformation is derived. The coupled dynamic responses of sandwich beams with different core strengths are investigated. The results indicate that this model improves the prediction accuracy of the responses of the sandwich beams, and is available for the situation when the sandwich beam undergoes moderate global deformation.