A new method which couples the level set method with meshless method to simulate crack growth is presented. The coupling of level set and meshless method can achieve naturally because they all set up based on the discrete nodal data. Two level sets that are orthogonal to one another at the crack tip are used to represent the geometry of crack and the location of crack tip

and to construct the Heaviside skip function and the Westergaard enriched function near the crack tip in the element-free Galerkin method (EFGM) discontinuous approximation. New crack tips are defined by the update algorithm of level set easily when the crack is growing. The coupling method does not use the visibility method

the diffraction method or the transparency method. The singularity is reproduced very well; and the convergence for elastic problems is improved. The passage of crack has no influence on the nodal domain. Smaller domain is used to calculation

which keeps the band and sparsity of the over all stiffness matrix. In addition

the level set makes the selection of enriched nodes and the establishment of additional function simply; and its update process needs no evolution equations. The numerical results show that the presented method has higher computational accuracy; and the simulated expanding path of crack is coincided with the tested curve. So

the results verify the validity and accuracy of the presented method.