The present study deals with the influence of residual stresses induced by the buried-arc welding on the crack behavior in two butt-welded 20 mm thick plates. The following steps were undertaken: the thermo-mechanical simulation of the welding process, the mapping of stress results from a finite element (FE) mesh used for the welding simulation to a new FE mesh with a crack, the stress balancing, and the stress intensity factor (SIF) calculation. The FE and weight function (WF) methods were used to investigate the SIFs at the deepest point of semi-elliptical surface cracks with different geometries, orientations, and positions in relation to the weld line. In the case of cracks perpendicular to the weld line, the FE and WF results showed a good agreement for smaller cracks, while deviation between the results increases with the size of the crack. Considering the SIF solutions for the cracks of arbitrary orientation, it was observed that for some cases, the SIF value for mode III of crack opening can be of significant influence.