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The rather complex 3D fatigue crack growth behaviour of two anti-symmetric “bird wing” cracks, initiating from the two crack front corner points of anotched shaft undergoing torsion, is investigated by the Dual Boundary ElementMethod (DBEM) and by two different approaches with the Finite Element Method(FEM). In order to calculate the Stress Intensity Factors (SIFs) along the crack frontfour different methods are utilised: COD and J-integral in conjunction with the DBEMand the Quarter Point Element Stress method or the Modified Virtual Crack ClosureIntegral method in conjunction with the FEM approaches. The SIFs, calculated by suchdifferent approaches, are well consistent with each other and the simulated crack paths,based on different fracture criteria (Minimum Strain Energy Density for DBEM and ’criterion for one of the FEM approaches) qualitatively agree well among themselvesand with the experimental findings.