Abstarct: Fracture mechanics is one of the most interesting subjects for prominent researchers. In fact the combination of the fracture mechanics and the numerical methods has been appealing for scientists. Finite difference, finite element method, boundary element method, meshless methods and the discrete element methods have utilized since last few decades. Among these numerical approaches the isogeometric analysis method is chosen due to its inherit specifications in the computational fracture mechanics. An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-baxsed isogeometric analysis method is investigated. The interaction integral method is baxsed on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis functions the possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric analysis method a suitable candidate for modelling discrete cracks. Also repetition of two different control points between two patches can create a discontinuity and also demonstrates a singularity in the stiffness matrix. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. Various numerical simulations for edge and center cracks demonstrate the suitability of the isogeometric analysis approach to fracture mechanics. Also, due to evaluation the isogeometric analysis results the extended finite element method is coupled with the level set method to create all kind of discontinuities. In other words, where the IGA can not fulfil the objectives of the fracture mechanics calculations for example in the internal discontinuity boundaries modelling such as circular holes and soft or hard inclusions, the XFEM is utilized. All results are shown the capabilities of isogeometric analysis method and also the extended finite element mthod in all catagories of the computational fracture mechanics.