An automatic 3D crack growth algorithm for fatigue crack propagation of arbitrary three dimensional problems with linear-elastic material behavior is presented. The stress analysis is based on a special BEM formulation –- the 3D Dual Discontinuity Method (DDM) –- which is advantageous for modelling propagating cracks. An optimized evaluation of very accurate SIF's and T-stresses along the whole crack front and the knowledge of 3D corner singularities are the basis of the proposed 3D crack growth criterion. The criterion is a predictor-corrector procedure taking into account the T-stresses and the often missing $K_{\rm III}$ in addition to $K_{\rm I}$ and $K_{\rm II}$ for the calculation of the kink angle. Moreover, a 3D singularity analysis is performed ensuring a valid square-root singularity along the crack front, especially in the vicinity of the intersection with the free surface. This guarantees a bounded energy release rate. Finally, the high level of automatization is accomplished by a sophisticated re-meshing algorithm for the update of the numerical model.