Abstract: In this paper, the lattice model and statistical distributions are used to represent the initial heterogeneous distribution of material properties. Equations of the reduplicate multi-sub-region (RMSR) boundary element method are established for the lattice model of 2-D heterogeneous materials. Each row of sub-regions in the lattice are integrated into a super-sub-region and the transfer matrix of sub-region method (TMSRM) is employed to solve the super-sub-region placed in chain. Since the memory demand of the TMSRM is only a little more than that of solving one super-sub-region and the coefficient matrices are only generated just once in RMSR, the capacity and efficiency can be increased significantly. As an example of application of the above-proposed methods, the failure process of 2-D heterogeneous materials is numerically simulated. With the RMSR and TMSRM, the continuous distribution of stress with high accuracy is expected, which provides a good foundation for further research on the initiation, propagation of crack and failure process in heterogeneous materials.