The aim of the present thesis is to provide a numerical tool for the mechanical modeling of dynamic failure in concrete. This widely used construction material is characterized by a non-linear failure behavior, which is consequently difficult to describe with macroscopic quantities. In order to grasp the mechanical damage response of this heterogeneous brittle material, our approach is based on a meso-mechanical point of view. The whole research work is, therefore, mainly focused on the understanding of the mechanisms that are linked with the material’s heterogeneous composition. The advantage of this level of observation is that it allows to represent the most important concrete constituents (e.g. aggregates and cement paste), thus facilitating the physical identification of the material parameters of the model and of the mechanisms (interaction between matrix and inclusions) that characterize its constitutive behavior. For this purpose we exploit the capabilities of a two-dimensional finite-element model. The onset of fracture is explicitly modeled using the well-known cohesive approach. We first investigate the dynamic tensile response of concrete specimens. Different simulations are carried out to assess the influence of aggregates properties on peak strength and dissipated fracture energy at different strain rates. The model aims to explain the strain-rate strengthening through structural effects. However, to capture the full extent observed experimentally, our results suggest that is not possible to discard the combination of inertial with material rate hardening mechanisms. Next, in order to account for crack-interactions as well as path dependent behavior, the model is enriched with the introduction of an explicit contact algorithm and a mode-dependent fracture energy. To demonstrate the capability of the proposed approach to provide accurate results, the model is first applied to two benchmark tests in masonry engineering. Afterwards, the developed framework is applied to reproduce dynamic compressive failure of meso-scale concrete samples. Simulations involving different strain rates and levels of lateral confinement are conducted. An energetic analysis shows that dissipation of energy through fracture and friction is an increasing function of the applied confinement and strain rate. Our results underline thus the importance of capturing frictional mechanisms, which appear to dissipate a raising amount of frictional energy with increasing strain and applied pressure. Finally, a multi-scale computational framework is developed to up scale the obtained fine scale response to the coarse scale. The selected approach considers concrete macroscopically as being homogeneous and to behave linear elastically aside from the propagating cracks. The cohesive macroscopic tractions are however extracted from the response of meso-scale representative volume elements, which are activated on the fly when a macroscopic discontinuity propagates. Parallel simulation shows the capability of the model to predict the structural response of a tested unit including the physical mechanisms occurring at the fine scale.