Solutions are obtained for the large plastic deformations of cylindrical membrane shells under internal pressure. Comparisons are made of the results given by incremental and deformation theories for a material obeying the Mises yield condition and which strain hardens according to the power law σ = K ɛ n. These comparisons show close agreement between the results of the two theories even for eases in which large variations in the stress biaxiality ratio occur during deformation. The accuracy of the approximate deformation theory solution proposed by Weil is shown to be satisfactory for the range of cases considered. The results of tests of three mild steel cylinders with radius-thickness ratios of approximately 40 and length-diameter ratios of 0.547, 1.02, and 2.01 are given. Comparisons of the results of these tests with both exact and approximate theories are made and the agreement found to be satisfactory in all cases.