New solutions were developed for the stress intensity factor and the crack opening displacement at the crack center for the semi-elliptical surface crack in a wide plate under remote tension and bending loads. The solutions were based on results of finite element analyses made by an automated program system and the accuracy of the results was carefully studied. The new solutions were used for developing weight functions for the structure. The accuracy of these weight functions was tested by analyzing several loading cases. The present automated finite element analysis of surface cracks can be applied to practically any structural geometry and the results can be applied in developing a weight function for the case. This was demonstrated by developing a weight function for a surface crack in a weld connecting a nozzle to a pressure vessel. The accuracy of the present weight function method is sufficient for practical applications.