Particle packing on meso-level has a significant influence on workability of fresh concrete and also on the mechanical and durability properties of the matured material. It was demonstrated earlier that shape exerts but a marginal influence on the elastic properties of concrete provided being packed to the same density, which is not necessarily the case with different types of aggregate. Hence, elastic properties of concrete can be treated as approximately structure-insensitive parameters. However, fracture behaviour can be expected structure-sensitive. This is supported by the present study based on discrete element method (DEM) simulated three-phase concrete, namely aggregate, matrix and interfacial transition zones (ITZs). Fracture properties are assessed with the aid of a finite element method (FEM) based on the damage materials model. Effects on tensile strength due to grain shape and packing density are investigated. Shape differences are shown to have only modest influence. Significant effects are exerted by packing density and physical-mechanical properties of the phases, whereby the ITZ takes up a major position.