An understanding of the response and failure of reinforced concrete structures subjected to impact loadings is of great importance in safety calculations and assessment in civil as well as defence engineering. In this paper, a numerical study is performed on the impact response of reinforced concrete beams by a newly proposed 3D meso-mechanical model together with a recently developed computational dynamic constitutive model for concrete. In the 3D meso-mechanical model, concrete is considered as a three-phase composite material consisting of mortar matrix, coarse aggregates and interfacial transition zone (ITZ layers). The constitutive model for concrete takes into account pressure dependency, shear damage, tensile softening, Lode effect and strain rate effect, etc. It is shown that the numerical results are in good agreement with the experimental observations in terms of time histories of impact force and displacement as well as crack distribution and propagation and that the newly developed 3D meso-mechanical model together with the previously proposed constitutive model for concrete can be used to predict the response and failure of reinforced concrete structures subjected to impact loading.