To study the bending strength of mass concrete under dynamic loading, the pure bending zone of three-graded concrete beam is considered as a three-phase composite composed of matrix, aggregate and interface between them on meso-level. Dynamic constitutive model considering strain-rate strengthening effect and damage softening effect is adopted to describe the cocrete and meso-element's damage. The failure mechanisms of beam under impact loading, triagle wave load, dynamic load coupling with initial static loading were simulated by using displacement-controlled FEM. Furthermore, stress-strain curve of the specimens and their dynamic bending strength were obtained. The results obtained from numerical simulation agreed well with experimental data.