Abstract: To overcome some inherent flaws and improve accuracy of the finite element method (FEM)， a novel numerical method called cell-based smoothed extended finite element method (CS-XFEM) was presented. It combined the cell-based smoothed finite element method (CSFEM) and the extended finite element method (XFEM). The CS-XFEM was used to simulate an orthotropic plate containing center crack or inclined crack， and then was compared with FEM， XFEM and bimaterial extended finite element method (BXFEM). The result shows that the CS-XFEM has the advantages of both the CSFEM and XFEM: the meshes are independent to the crack surface; the end of crack needn’t to be a node and the meshes around the end needn’t to be fined; the CS-XFEM can transform domain integration into boundary integration， therefore， the derivatives of the shape functions are not needed and the mesh size needn’t to be regular. The CS-XFEM is a simple and efficient numerical method to analyze fracture problems.

Key words: numerical calculation, CS-XFEM, orthotropic, XFEM, stress intensity factor