A comprehensive numerical study in which a large number of Mode I stress intensity factor (KI) solutions for cracks in plates and shells were generated for inclusion in the American Petroleum Institute (API) Recommended Practice on Fitness-For-Service (RP 579). A series of 2D and 3D finite element analyses were performed on plates, cylinders, and spheres containing surface cracks and buried cracks. A wide range of flaw aspect rati's at radius/thickness rati's were considered. The results of these analyses are tabulated in the present report as well as Appendix C of API RP 579.This report also describes a weight function methodology in which KI solutions for arbitrary through-wall stress distributions can be derived for surface cracks in plates and shells. The weight function for a given geometry and crack size is derived from reference solutions for uniform and linear crack-face pressure. The necessary reference KI solutions for surface cracks in plates, cylinders and spheres are provided in the present report.