The state of the art, criteria, and recommended practices for the theoretical and experimental analyses of discontinuity stresses and their distribution in metallic pressure vessels for space vehicles are outlined. The applicable types of pressure vessels include propellant tanks ranging from main load-carrying integral tank structure to small auxiliary tanks, storage tanks, solid propellant motor cases, high pressure gas bottles, and pressurized cabins. The major sources of discontinuity stresses are discussed, including deviations in geometry, material properties, loads, and temperature. The advantages, limitations, and disadvantages of various theoretical and experimental discontinuity analysis methods are summarized. Guides are presented for evaluating discontinuity stresses so that pressure vessel performance will not fall below acceptable levels.