The analysis of stresses in pressure vessels has had a long and active history. Its development has, naturally, been tied to and kept pace with the advancement of the theory of shells. The basic equations which govern the stresses in an elastic shell, such as a pressure vessel and its heads, were derived in 1888 by Love. Some early solutions of these equations, which were directly applicable to pressure vessel analysis, were carried out by H. Ressiner, Meissner, and their students at the turn of the century. This involved studies of spherical, conical, and toroidal shells of revolution by Dubois, Honegger, Bolle, and Wissler. The arduous hand computations that were involved in these remarkably detailed efforts were, and still are, however, prohibitive as far as the pressure vessel design process is concerned. Engineers, therefore, turned to the development of approximate techniques in which the analytical and computational labor could be reduced. This search led, among other methods, to the well-known membrane approximation in which the resistance of the shell to bending is ignored. This method of analysis greatly simplifies the calculation of stresses in shells and improves in accuracy as the shell becomes thinner. It found its way into the ASME Code for Unfired Pressure Vessels and has been firmly lodged therein until recently. The chief shortcoming of the method is that it introduces inconsistencies and thereby incorrectly predicts the stresses at junctions between mating shells, at points of support and at local sources bending. On the basis of these limitations Watts and Burrows urged a return to the use of the original theory with bending resistance included in 1949. As a result the Pressure Vessel Research Committee embarked upon a program in which cylindrical pressure vessels with various heads were analyzed within the framework of Love's original theory.