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Pressure vessel analysts and designers have long made use of shell theory to solve their problems. Various types of shell theories have been proposed in the literature. These theories are in wide use, but because of their appropximate character they often lead to failures which could have been predicted only on the basis of more refined theories. However, even the so-called refined theories are themselves dreived from the exact three-dimensional elasticity equations on the basis of artificial assumptions whose validity is often open to question. Moreover, in the process of making these assumptions certain contradictions occur which have resulted in shell theories of great variety and complexity. The present paper discusses the inherent assumptions and range of applicability of various simplified shell theories which are employed in the linear analysis of their pressure vessels. Via the problem of the line load along a generator, it is shown how to obtain the complete solution through a proper superposition of the solutions from the simplified theories.