Industry design standards such as BS 7910 deployed some empirical formulas for the prediction of stress intensity factor (SIF) based on simulation results from traditional finite element method (FEM). However, such FEM simulation occasionally failed to convince people due to the large discrepancies compared with engineering practice. As a consequence, inaccuracy predictions via such formulas in engineering standards inevitably occur, which will compromise the safety of structures. In our previous research work, an abnormal phenomenon of SIF in a cracked T-butt joint accounting for welding effect has been observed. Compared with BS 7910, the calculation results of SIF at the surface points of welded specimens cannot be well predicted, with a large discrepancy appearing. In order to explore such problem with an abnormal increase at the surface points of cracked welded specimens, a numerical investigation in terms of SIF among BS 7910, XFEM, and FEM is performed in this paper. Numerical models on both a simple cracked plate without welding effect and a cracked T-butt joint with welding effect are developed through ABAQUS. Parametric studies in terms of the effects of varied crack depth to thickness ratio (a/T) and the effects of crack depth to crack half-length ratio (a/c) are carried out. Empirical solutions from BS 7910 are used for comparison. It is found that the XFEM can provide predictions of SIF at both the crack deepest point and crack surface point of a simple cracked plate as accurate as FEM. For a T-butt joint with a transverse stiffener, a large discrepancy in terms of the weld magnification factors (M_k) occurs at the crack surface point compared with empirical predictions. An exceptional increase of von Mises stress gradient in regions close to the weld-toe is found through the simulation of FEM, whereas a constant stress gradient is obtained through XFEM. The comparison results indicate an inappropriate prediction of SIF by the utilization of the empirical formulas in BS 7910. A more reasonable prediction of the SIF at the surface point of a crack is obtained by the XFEM. Therefore, further updating of the empirical solutions in BS 7910 for SIF accounting for welding effect is recommended.