At the mesoscopic scale, concrete can be considered as a mix of coarse aggregates with a mortar paste matrix. In this paper, we investigate numerically the influence of aggregates arrangements and loading rate on the tensile response of concrete. Each coarse aggregate is assumed to be circular with six different radiuses following the aggregates size distribution of real gravel. Rate-independent cohesive elements are used to model failure within the mesostructure. Our results show that the spatial distribution of heterogeneities does not influence the peak strength, while it changes the post-peak macroscopic response. This implies that our specimen size is large enough for strength computation but that larger mesostructures should be considered to obtain fully reliable toughness predictions. Although the cohesive approach is able to capture the transition from one macro-crack in quasi-static to multiple micro-cracks in fast dynamics, which increases the dissipated fracture energy, our results suggest that the full extent of the high-rate strengthening of concrete observed experimentally for loading rates greater than 1/s cannot be captured with rate independent constitutive laws.Copyright © 2013 John Wiley & Sons, Ltd.