The present work investigates the effect of the elliptical three-dimensional (3D) cracks on a pipe with thickness transition, considering internal pressure. Level sets were defined using the extended finite element method (XFEM), the stress intensity factors (SIFs) of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition. The results show that the XFEM is an effective tool for modeling crack in pipes. A pressurized pipe with thickness transition is more sensitive to the feature compared to the straight pipe. Parameters of the transition zone have an influence on stress intensity factors. Quantification of the SIFs associated with cracks in the transition zone of pipes with thicknesses is performed.