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Various methods and theories of failure have been used to determine the wall thickness of pressure vessels.These theories and methods are based upon simple tensile yield strength or ultimate strength and have been thoroughly reviewed by Burrows. In using simple tensile yield or ultimate strengths but with different ductilities are equally satisfactory to the designer. In other words, the determination of the failure load for a pressure vessel should consider the plastic stress-strain behavior of the material to failure. This paper develops a theory for finding the wall thickness of a thin-walled cylindrical pressure vessel based upon the plastic range and so-called "instability" or maximum pressure that can be produced in the vessel.