This paper presents a computational framework for modelling the fracture process in concrete under static and dynamic tensile loading considering its mesostructural characteristics. 3D mesostructure of concrete composed of real-shape coarse aggregates, mortar, interfacial transition zone between them and voids was developed using an in-house code based on Voronoi tessellation and splining techniques. Cohesive zone model was then employed to simulate the tensile fracture behaviour of concrete in terms of stress- and energy dissipation-displacement responses and crack mechanisms against the shape (spherical and irregular) and volume fraction (30%, 35% and 40%) of aggregate and strain rate (0, 1, 10 and 50 s−1). Results indicate that the irregular shape of aggregate has an important role in the micro-crack nucleation and ultimate fracture pattern but exhibits an insignificant effect on the tensile strength of concrete, which is mainly dependent on the strain rate and the random location and size distribution of aggregate.