In this study, the extended element free Galerkin method (XEFG) is used for crack analysis an edge crack parallel to the material variation in a rectangular functionally graded material (FGM) plate under traction loading. For the first time, the effective parameters of XEFGM are employed such as the sub-triangulation term for numerical integration, suitable influence domain, and enrichment functions for discontinues locations in the fracture analysis of different crack positions of an edge cracked FGM plate. In addition, the incompatible formulation is adopted to extract the stress intensity factors (SIFs). Good data and results are observed about the relationship between the crack lengths and SIFs with good verification during changing XEFG parameters. There is good agreement and stability in the results of SIFs through the sizes of J-integral rJ equal to 0.4 -0.8. In addition, the acceptance results for the size of the support domain are bound between dmax=1.52 to 2.