This paper presents the moment-curvature relationship and the components of displacement in the cross section of a uniformly pressurized, long, closed, circular, cylindrical shell. The shell is loaded in one of its principal planes by two equal and opposite terminal couples: First, the shell undergoes small initial displacements. These are formed by superimposing pressurization displacements upon Saint Venant displacements. Second, from this deformed position the shell is perturbed into a system of additional small displacements. A Rayleigh-Ritz technique is used to find the latter displacements from the theorem of minimum potential energy. The point at which the moment-curvature relationship becomes nonlinear is shown by several curves in this paper.