This paper presents a numerical strategy for realistic modelling of the internal material configuration and cracking of concrete on mesoscale. Polyhedron shapes resembling crushed rocks are adopted to represent the aggregate. A packing approach in which the particles are heaped up layer by layer is proposed for 3-D condition. A cubic representative volume element (RVE) is generated using the method. The cohesive approach, in which zero thickness cohesive elements are inserted into the ordinary finite element mesh along the potential cracking path, is adopted to model the cracking developing process. The cracking behaviours of created RVE under uniaxial tension are well simulated using the current approach.