**Abstract**

This research describes crack analysis in the functionally graded materials (FGMs) by adopting the extended element free Galerkin method (XEFGM) under mixed mode and asymmetric loading. These loads are somewhat similar to fatigue loads because, numerically, they are load values from zero and then directly to the critical load. The meshfree method can be easily simulated the fracture problems against the traditional numerical method because it is not dependent on mesh. Triangles technique in the process of numerical integration at regions of discontinuity, functions of enrichment, and as well as the appropriate support field to contain numerical points and nodes to from the shape functions are used in this study. In addition, incompatible interaction integration technique has used to determine the stress intensity factors (SIFs). Two study cases with different crack positions were studied and compared with the experimental works of the relevant reference literature, where accurate and identical results were obtained.

**Keywords:** Crack propagation, incompatible interaction integration technique, meshfree method, functionally graded materials
