A numerical method from the mesoscopic point of view is proposed to describe the fracture process of concrete. At mesoscopic level, concrete is considered as a three-phase composite consisting of mortar matrix, coarse aggregate and interfacial transition zone (ITZ) between them. According to the grading of coarse aggregate obtained from sieve analysis, the random aggregate models with polygonal aggregates were generated by Monte Carlo random sampling principle. In this work, the tensile cracking is assumed to the only failure criterion at the mesoscopic scale; and the stress-separation law based on the fictitious crack model is adopted to allay the sensitivity on mesh size in the softening regime. The nonlinear finite element method is used in the simulation of concrete under bend loading. The influence of the shape of aggregate on the macroscopic response of concrete is also investigated. Numerical results show that the strength of the specimen with circular aggregate is higher than the specimen with arbitrary polygonal aggregate. The predicted bending strength agrees well with experimental data.