The BOSOR5 computer program is used to predict buckling loads of forty axially compressed mild steel cylindrical shells tested in 1974 at the Chicago Bridge & Iron Company. The 15-inch-diameter shells have radius-to-thickness ratios of 500, 375, and 250. With imperfections neglected the average ratio of theoretical buckling load to test buckling load is 1.28 with a standard deviation of 0.145. All of the perfect shells are predicted to buckle by axisymmetric collapse rather than by nonsymmetric bifurcation buckling, a result consistent with Bijlaard's theory (1949). With axisymmetric imperfections included in the analysis, the average ratio of theoretical buckling load to test load is 1.005 with a standard deviation of 0.118. With axisymmetric imperfections included in the analysis, the unstiffened shells and the specimens with rings spaced more than 1.5 times the wavelength corresponding to axisymmetric buckling of an unstiffened shell, buckle nonsymmetrically in a manner analogous to that predicted by Koiter's theory for elastic shells (1963) and Gellin's theory for elastic-plastic shells (1979). Axisymmetrically imperfect shells with rings spaced more closely buckle by axisymmetric collapse in most cases and by general nonaxisymmetric instability of both rings and shell in a few cases. Inclusion of axisymmetric imperfections in the analytical models leads to predicted variations of buckling behavior with ring spacing and ring cross section that agree qualitatively with those observed in the tests. Inclusion of plasticity considerably lowers the buckling loads, even though the average axial stress is in the elastic range, a result consistent with the theories of Donnell (1934) and Mayers and Meller (1972). Residual strains due to cold forming of the cylinders from flat sheets have a negligible effect on the critical loads. The largest scatter corresponds, surprisingly, to specimens with the closest ring spacing. It is surmised that in these configurations the buckling loads are especially sensitive to circumferential variation of the axial load and residual stresses and deformations associated with fitting of the rings to the shells.