Abstract: The fracture problem of the functionally graded material (FGM) is analyzed using the element-free method (EFM). Basing on the moving least-squares approximation, the node distribution in EFM is very free. This kind of interpolation better reflects the deformation. EFM can conveniently adopt the material properties of the integration point to analyze FGM. Numerical results show that EFM has high efficiency, accuracy and flexibility when studying FGM.