Abstract: A numerical approach based on Beam-Particle Model (BPM²) is developed to the simulation of fracture process of concrete samples under uniaxial compression. Three types of beam have been used in BPM² to form numerical model of concrete at mesoscale level, and the mechanical properties of every type of beam are randomly initialized according to Weibull distribution so as to reflect the initial heterogeneity of concrete samples at mesoscale level. The results of numerical simulation showed that the initiation and propagation of internal cracks at mesoscale level and their connection with each other in the concrete samples are just the cause of its macro-failure. It has been revealed via a comparison of numerical simulations that the failure modes of concrete samples vary with the initial heterogeneity of distribution of material properties. The fracture mechanism of concrete has been discussed on the basis of the numerical simulation.