The two most promising approaches to determine Stress Intensity Factor (SIF) developed over the past decade are the Symmetric Galerkin Boundary Element Method - Finite Element Method (SGBEM-FEM) based alternating method and the Extended Finite Element (XFEM) method. The purpose of this paper is to determine the SIFs for a number of 2-D crack problems by the two approaches and measure their relative effectiveness in terms of accuracy, speed and computational resources. In the SGBEM-FEM alternating method, a finite element analysis is carried out on the un-cracked body using the externally applied loading and next a boundary element analysis is performed by reversing the stresses found on the crack location from the finite element analysis, and the residual stresses on the boundary of the finite body are determined. The steps are repeated until convergence is achieved where the residual stresses on the boundaries and traction on the crack surfaces are close to zero. In the XFEM method, the mesh is created without considering the topology of the crack configuration and the discontinuities are handled by special discontinuity enrichment functions. The enrichment functions increase the degrees of freedom and the regular stiffness matrix is augmented by additional terms corresponding to the extra degrees of freedom but the increase in computational requirement is offset by not having the burden of remeshing the finite elements. Both SGBEM method and XFEM method are used to solve a number of crack problems and the example cases clearly show the computational efficiency of the SGBEM method over the XFEM method.