Abstract: The element displacement modes of the extended finite element method for plane crack problems are discussed in this paper. The governing equations for the extended finite element method are derived based on the principle of virtual work. The numerical integration technique is adopted for special elements. The displacement extrapolation method is formulated to calculate the stress intensity factor based on the least square method. The numerical computation programs are developed by using the MATLAB, and the numerical calculations are carried out by the extended finite element method for the problem of plane crack. Based on the results of the extended finite element method, the stress intensity factors of plane crack are calculated by the displacement extrapolation method and the interaction integral method, respectively. Numerical results show that with the displacement extrapolation method, the stress intensity factors can be obtained more easily and precisely than the interaction integral method.