Abstract: The mechanical behavior of concrete depends on the geometry size of the member, generally called size effect. This paper takes concrete as a three-phase composite material consisting of coarse aggregates, mortar matrix and interfacial transition zone between the aggregate and the mortar. In terms of such mesoscale assumption, numerical simulations on the size effect of splitting tensile strength and flexural compressive strength were carried out by means of the Rigid-Body-Spring Model (RBSM). The calculated results were then compared with test data from the available literatures. It is shown that both the failure patterns and splitting tensile strength are in good agreement with those from the experiments, and the size effect is more apparent in smaller size samples. The flexural compressive strength of concrete was evaluated on the basis of the mid-span cross-section of a four-point bending reinforced concrete (RC) beam. From the numerical results, it is found that the nominal compressive strength becomes lower with the increasing of the effective depth of RC beams, and keeps relatively stable when the effective depths are larger than 240mm.