Objectives: Numerical determinations of Stress Intensity Factors (SIFs) for a shaft under mixed-mode load with a crack of different sizes in the connection zone between square and circular cross-sections. Methods: Linear-elastic Fracture Mechanics principles are used. The numerical analysis program used was ABAQUS CAE version 6.9-3. The shaft consists in a circular section and a square section, with a fillet connecting zone. Cracks of different lengths and different depths are modeled. The shaft is subjected to torsion and bending. The SIFs were determined using the contour integral method. Results: The stress distribution was determined and plotted, and the stress concentration effect of the notches was highlighted. Crack propagation was also performed, using the XFEM module of ABAQUS code. The computed SIFs were plotted along the crack front. Conclusions: Crack initiation and propagation matched the pattern obtained in experimental tests, thus validating the model. The results confirmed that the fillet zone between the two sections acts as a stress concentrator. The fillet radius determines the magnitude of stress concentration. Crack geometry has a significant influence on SIFs, as well as on the global stress distribution.