We investigate the feasibility of using cohesive theories of fracture, in conjunction with the direct simulation of fracture and fragmentation, in order to describe processes of tensile damage and compressive crushing in concrete specimens subjected to dynamic loading. We account explicitly for microcracking, the development of macroscopic cracks and inertia, and the e ective dynamic behaviour of the material is predicted as an outcome of the calculations. The cohesive properties of the material are assumed to be rate-independent and are therefore determined by static properties such as the static tensile strength. The ability of model to predict the dynamic behaviour of concrete may be traced to the fact that cohesive theories endow the material with an intrinsic time scale. The particular conรฟguration contemplated in this study is the Brazilian cylinder test performed in a Hopkinson bar. Our simulations capture closely the experimentally observed rate sensitivity of the dynamic strength of concrete in the form of a nearly linear increase in dynamic strength with strain rate. More generally, our simulations give accurate transmitted loads over a range of strain rates, which attests to the รฟdelity of the model where rate e ects are concerned. The model also predicts key features of the fracture pattern such as the primary lens-shaped cracks parallel to the load plane, as well as the secondary profuse cracking near the supports. The primary cracks are predicted to be nucleated at the centre of the circular bases of the cylinder and to subsequently propagate towards the interior, in accordance with experimental observations. The primary and secondary cracks are responsible for two peaks in the load history, also in keeping with experiment. The results of the simulations also exhibit a size e ect. These results validate the theory as it bears on mixed-mode fracture and fragmentation processes in concrete over a range of strain rates.