Tanks in the form of a surface of revolution are sometimes employed for carrying fuel. The purpose of this paper is to show how the stresses, due to the internal hydrostatic pressure, in a shell of this kind can be calculated when the equation of the generating curve is given. The acceleration imposed on the shell and its contents will be assumed to be at right angles to the axis of revolution, hence shear as well as direct stresses are set up. It will be supposed that no longitudinal bulkheads are fitted, and the shell will be taken as very thin so that the bending stresses in it are negligible. No attempt will be made to examine the stress distribution in the neighbourhood of a relatively rigid supporting ring; as shown by Timoshenko these ‘ end effects ’ are appreciable only in the immediate vicinity of the support. Nor will the stability be considered of those portions of the shell which are subjected to compression. Thus attention will be confined to what are commonly described as the membrane stresses.