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A new numerical approach was developed to study the mechanical properties of cementitious granular materials. At first, an ellipsoid based method was developed to generate aggregate particles of arbitrary shape. These aggregate particles were then mixed in a cement paste using the algorithm-based program HADES and an interfacial transition zone (ITZ) between the aggregate particles and the cement paste was added. All phases including aggregate, cement paste and ITZ were meshed by a special tool Gmsh. The mesh data was transferred into the finite element code, Finite Element Analysis Program (FEAP) to predict the mechanical properties of the material. As a typical cementitious granular material, concrete was simulated using this approach. The method was also validated by way of comparison to existing results available in previous studies of concrete. 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 effective in predicting the elastic modulus of three-phase cementitious granular materials (cement paste, ITZ and aggregate).