The corner point singularity of surface cracks by finite element method (FEM) has become a numerical concern decades ago. The literature showed that the stress intensity factors (SIFs) at the corner points were often excluded. Further, most SIFs were reported for larger ratios of the crack depth over cylinder diameter. This paper presents the SIFs (Modes I, II and III) of a semi-elliptical surface crack at a solid round bar under torsion. The tetrahedral and hexahedral elements were used in the finite element modelling. The effects of the loading mode and the crack aspect ratio on the corner point singularity were discussed. The tetrahedral meshing was generally observed to be more suitable for modelling relatively small surface cracks, particularly in respect to the corner point singularity. For all loading modes, the SIFs away from the corner points of using the tetrahedral meshing were found to have fairly good agreement with those by dual boundary element method (DBEM).