Abstract: The newly developed Polygon Scaled Boundary Finite Elements (PSBFE) combining with topography-based local remeshing technique is, for the first time, applied to the fracture analysis of composite materials. Near-interfacial crack propagation in a layered metal-ceramic structure is simulated and the effects of elastic constants mismatch on the interaction between a propagating crack and a single inclusion in brittle matrix materials are presented. The agreement between the simulating result, experimental and other numerical data available in literatures demonstrates a good validity and accuracy of the proposed method in predicting the crack-growth of composite material. The parametric study on the effect of mesh density and effect of different increments of crack propagation leads to the consistent results. This technique can represent the singular stress field at a crack tip more precisely than FEM. Meanwhile, it is more robust and universal than current crack growth simulation methods based on SBFEM.