Abstract: A newly proposed Meshless Shepard and Least Square (MSLS) interpolation has been employed for the simulation of crack growth. The MSLS shape function possesses the much desired Kronecker delta property. Thus the essential boundary conditions can be treated as easily as they are in Finite Element Method (FEM). The construction and derivation of the MSLS interpolation are also simpler than that of the Moving Least Square (MLS) approximation. This MSLS method overcomes the main difficulties of other meshless methods and is well-suited for the analysis of crack propagations. In this work, the contour integral method has been used to compute the mixed-mode stress intensity factors. The crack propagation angle is determined by the criterion of maximum stress in the tangential direction. Several numerical examples are presented to verify the validity and accuracy of the present method.