The more important theories and concepts involved in the analysis and design of vessels subjected to external pressure are reviewed and discussed. Using the analysis of one investigator as a foundation, an equation is formulated which is subsequently employed in the construction of charts for practical design. The charts will yield an optimum design with a safety factor of unity since they incorporate a parameter for out-of-roundness, a fabrication anomaly heretofore accounted for by the application of factors to classical perfect-shell theory. Ranges of design parameters and operating depths that will find primary usage in the field of underwater ordnance are covered. A typical design example of a pressure hull for an undersea weapon is presented in conclusion.