An enriched radial point interpolation meshless method(X-RPIM) was presented for the linear elastic fracture problem. In order to represent the discontinuous displacement field along crack face and stress singularity around the crack tip

enriched functions were added in the approximation of traditional radial point interpolation meshless method (RPIM) based on the ideas of partition of unity. The merit of presented method is that the shape functions have the properties of Kronecker δ functions

which would make the essential boundary be implemented easily. The construction of discontinuous approximation function

the discrete format of governing equation and the evaluated process of the mixed-mode stress intensity factors by using the J integral method are introduced in detail in X-RPIM. The impact for the computational results of stress intensity factors using different integral domains of crack tip is discussed. Analyses of numerical examples demonstrate that the enriched radial point interpolation meshless method can effectively solve fracture problem

and has practical merits for modeling crack growth problem.