Functionally graded materials (FGMs) exhibit continuous variations in composition along a specified direction, leading to spatial changes in mechanical and thermal properties. In orthotropic functionally graded materials, this behavior is further complicated by directional dependence, as material gradation interacts with orthotropic property variations along different axes. These anisotropic and non-uniform characteristics result in strongly direction-dependent mechanical responses, making accurate modeling and fracture prediction challenging. The element-free Galerkin method (EFGM) based on the Moving Least Squares Approximation (MLSA) is a widely used meshfree numerical technique for solving partial differential equations without requiring a predefined mesh, unlike the finite element method (FEM). Although EFGM has been successfully applied to FGM problems involving strong discontinuities, the non-interpolatory nature of MLSA shape functions leads to approximate enforcement of essential boundary conditions (EBCs) and ill-conditioned solutions due to singular moment matrices[1]. In the present study, the applicability of the Interpolating Modified Moving Least Squares (IMMLS) method is investigated for solving fracture mechanics problems in FGMs [2]. The IMMLS-based EFGM possesses inherent interpolating shape functions, enabling exact enforcement of EBCs and yielding a unique and stable solution [1]. Using this framework, various crack configurations ---including straight, inclined, and multiple cracks --- in functionally graded domains are modeled for regular and irregular nodal configuration to compute stress intensity factors using J-intergral method. A comparative study between MLSA- and IMMLS-based EFGM for FGM structures is carried out to evaluate improvements in accuracy and computational efficiency over the MLSA approach. Validation against benchmark problems demonstrates excellent performance, with mean percentage deviations ranging from 1.0% to 5.0% across different test cases. REFERENCES [1] S. K. Lohit, Amar K. Gaonkar, Tejas P. Gotkhindi. Anisotropic magneto-electro-elastic fracture mechanics in orthotropic materials: Analysis using efficient interpolating modified MLS-based EFGMs and interaction integral. Engineering Fracture Mechanics, 111350, 2025. [2] B. N. Rao, S. Rahman. Mesh-free analysis of cracks in isotropic functionally graded materials. Engineering Fracture Mechanics. 70(1), 1-27, 2003