The safety of externally pressurized manned diving bells, submersibles and underwater work systems resides in the ability of the system to rise to the surface in case of an emergency. Use of the ASME Boiler and Pressure Vessel Code Section VIII design rules, lead to unacceptably heavy structures, and thus substantially compromise the sought-for safety in underwater manned systems. A recognition on the part of the diving industry of the inherent limitations in using the ASME Boiler and Pressure Vessel Code for design of underwater pressure vessels, motivated the formation of the ASME Safety Code Committee on Pressure Vessels for Human Occupancy (PVHO) in 1974. A subcommittee of the PVHO Safety Code Committee was formed to address the specific problems of external pressure vessel design. The mathematical development which provided the basis for the proposed rules are presented. The restrictions imposed by the External Pressure Subcommittee are also presented.