Cementitious materials can be considered as consisting of particulate elements on the levels of the microstructure and mesostructure. The mechanical properties of cementitious granular materials were studied by a numerical approach. First, an ellipsoid-based method was developed to generate single aggregate particles of arbitrary shape. The HADES toolbox was then used to form a material structure from aggregate (HADES is a concurrent, algorithm-based program that is designed to simulate the mixing or flow of granular material of arbitrary shape). Afterwards, an interfacial transition zone (ITZ) between the aggregate particles and the cement paste was enriched and a special tool, Gmsh, was used for forming a mesh of aggregate, cement paste, and ITZ. Finally, the mesh data was transferred into the finite element code FEAP to predict the mechanical properties of the material. Based on these processes, a simulation of concrete was used as an example of a typical cementitious granular material. Additionally, a parameter study was conducted to highlight the influence of aggregate on the mechanical properties. The simulation shows that the method is feasible and effectively predicts the elastic modulus of three-phase cementitious granular materials (cement paste, ITZ and aggregate).