Failure assessment of a pipe with a circumferential crack in a nuclear power plant has to conform to the Rules on Fitness for Service for Nuclear Power Plants published by JSME (The Japan Society of Mechanical Engineering)  in Japan. Based on the rules, the applied stresses considered in the failure assessment of the pipe using limit load assessment are membrane, bending, and thermal stresses. The failure assessment focuses only on mode I. In actual plants, depending on the piping system, there is a possibility that torsional stress  is applied to the pipe, in addition to membrane, bending, and thermal stresses. Under such a load condition, the crack opening mode will be mixed-mode. In ASME Boiler & Pressure Vessel Code section XI, the bending and torsional moment are considered in failure assessment of the pipe. Therefore, it is important to establish the failure assessment method for the pipe with the crack under mixed-mode. In this study, the XFEM (extended Finite Element Method)  was applied to assess failure of the austenitic stainless steel pipe (Type 304) with a circumferential crack subjected to bending and torsional moment. XFEM does not require elemental division considering the crack shape and its propagation path. Therefore, the time and cost for developing the analysis model can be reduced compared with conventional FEA (Finite Element Analysis). Fracture test results conducted under two conditions were used the analysis (Specimen No. TP1 and TP2) for determining the energy release rate for crack propagation and verifying the analysis results. The difference between the two tests was the ratio of torsional moment to bending moment. The ratios in TP1 and TP 2 were 0.6 and 1.2, respectively. A parametric analysis was conducted to determine the critical equivalent strain energy release rate required for crack initiation and propagation by comparison with TP1 results. The determined critical equivalent strain energy release rate was verified by comparison with TP2 results. In response to the above considerations, the decreasing load due to crack propagation in the fracture tests under mixed-mode condition was simulated by XFEM, and the maximum load, bending moment, and torsional moment were predicted within the margin of error of 6.1%.