In this paper, a recently developed meso-scale model, called the Lattice Discrete Particle Model (LDPM), is extended in order to include the effect of the loading rate on concrete strength and fracturing behavior. As verified experimentally, the rate dependence of concrete behavior is caused by two different physical mechanisms. The first is a dependence of the fracture process on the rate of crack opening, and the second is the viscoelastic deformation of the intact (unfractured) cement paste. For concrete both mechanisms are important but the former dominates at extreme strain rates under impact. In this study, the first mechanism is described by the activation energy theory applied to the ruptures that occur along the crack surfaces. The developed model will be calibrated and validated on the basis of experimental data available in the literature. In particular numerical simulations of 1) impact tests on prismatic specimens in compression, and 2) dynamic Hopkinson bar tests in tension, are carried out. The numerical results show a very good agreement with the experimental results from both qualitative and quantitative points of view.