This paper presents a coupling technique for integrating the fractal finite element method (FFEM) with element free Galerkin method (EFGM) for analyzing homogeneous, isotropic, and two dimensional linear elastic cracked structures subjected to mode I loading condition. FFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprises both the element free Galerkin and the finite element shape functions, satisfies the consistency condition thus ensuring convergence of the proposed coupled FFEM-EFGM. The proposed method combines the best features of FFEM and EFGM, in the sense that no structured mesh or special enriched basis functions are necessary and no post processing (employing any path independent integrals) is needed to determine fracture parameters such as stress intensity factors (SIFs) and T-stress. The numerical results show that SIFs and T-stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack length to width ratio on the quality of the numerical solutions.