This report for RP1237-1 presents formulas, charts, and background material that allow calculation of safety margins in ductile structures containing flaws. It is intended as a reference book for engineers who are concerned with design and analysis of flawed structures. The work extends the analysis procedures already available for brittle elastic materials to the tough and ductile steels used in the construction of pressure-boundary components. These new elastic-plastic methods more accurately describe the behavior of ductile materials and show more tolerance to flaws than the elastic methods contained in the ASME Boiler and Pressure Vessel Code and the Code of Federal Regulations.