In the present study, in order to evaluate the elastic displacement field and subsequently the fracture parameters within the isotropic homogeneous elastic solids with the edge or interior cracks, the extended finite element method with level set technique was used to avoid the disadvantages associated with the standard finite element method. An overdeterministic least squares method was utilized to determine the crack stress intensity factors as well as the coefficients of the higher order terms in the Williams' asymptotic series solution for structures containing crack in various modes of failure by fitting the series solution of displacement fields around the crack tip to a large number of nodal displacements obtained from the extended finite element method. For validating the results, several cracked specimens subjected to pure mode I, pure mode II, and mixed modes I/II loading were performed. Comparisons with results available from the literature obtained by the other formulations reveal the efficiency and the simplicity of the proposed method and demonstrate the capability of it to capture accurately the crack stress intensity factors and the coefficients of higher order terms.