Abstract: Concrete is regarded as a two-phase composite constaining coarse aggregate particles and mortar matrix. The mortar matrix and coarse aggregate particles are assumed to be elastic, homogeneous and isotropic. Coarse aggregate particles are spherical. Based on the Mori-Tanaka concept of average stress and Eshelby equivalent inclusion theory, the elastic modulus of concrete is formulated. Using Horii and Nemat-Nasser sliding crack model of brittle materials subjected to biaxial compressive stress, the influences of micro-crack on elastic modulus and damage evolution are found out by the meso-mechanical method. A one-dimensional dynamic constitutive model of concrete subjected to impacting loading is established. It agrees well with the experimental results. So it can be used to simulate the dynamic mechanical behaviors of concrete under impact loading.