Concrete is non-homogeneous and is composed of three main constituent phases from a mesoscopic viewpoint, namely aggregates, mortar matrix, and interface transition zone (ITZ). A mesoscale model with explicit representation of the three distinctive phases is needed for investigation into the damage processes underlying the macroscopic behaviour of the composite material. This paper presents a full 3-D mesoscale finite element model for concrete. On top of the conventional take-and-place method, an additional process of creating supplementary aggregates is developed to overcome the low packing density problem associated with the take-and-place procedure. An advanced FE meshing solver is employed to mesh the highly unstructured domains. 3D mesoscale numerical simulation is then conducted for concrete specimen under different loading conditions, including dynamic loading with high strain rate. The results demonstrate that detailed mesoscopic damage processes can be realistically captured by the 3D mesoscale model while the macroscopic behaviour compares well with experimental observations under various stress conditions. The well-known inertial confinement effect under dynamic compression can be fully represented with the 3D mesoscale model and the trend of dynamic strength increase with strain rate from the 3D mesoscale analysis agrees well with the experimental data.