Abstract: The nonlinearity of macro-mechanical properties and the size effect of concrete are mainly caused by its heterogeneity. Considering the mesoscopic heterogeneity, meso-mechanical models were set up, which were composed of the aggregates, mortar matrix and interfacial transition zones (ITZ). The damage process of concrete cubic specimens subjected to splitting tensile loading was simulated, with cube side lengths including 150 mm, 250 mm, 350 mm and 450 mm. The effect of aggregate sizes (10 mm, 20 mm, 30 mm and 40 mm) on the mechanical properties and specimen size effect was studied. The simulated results were compared with test data. It was shown that the splitting tensile strength decreases slightly with an increase in aggregate size, however, once the aggregate size is increased to 30mm, this decline slows. There exists a size effect on splitting tensile strength for cubic specimens with different aggregate sizes. The specimens with small-sized aggregates become more brittle in the damage process than the specimens with big-sized aggregates. Therefore the size effect of specimens with small-sized aggregates is more obvious. The simulation data fit well with the size effect law proposed by Ba?ant and Weibull.