Circular cylindrical shells are prone to buckling failure under different types of external pressure. These can include uniform lateral pressure, hydrostatic pressure (uniform lateral plus end pressure), and non-uniform wind pressure. The focus of this study is to thoroughly examine the available formulas for calculating the buckling pressure of circular cylindrical shells under these various types of external pressure and to assess their limitations. The study delves into a dozen of simplified formulas drawn from literature, discussing their derivations and comparing them with the exact solution of the problem to unveil their constraints. The study also investigates the correlations between uniform lateral and wind pressures, the effects of geometrical and material nonlinearities, and the impact of imperfections. The findings confirm that hydrostatic buckling pressure is consistently lower than lateral buckling pressure, and the conditions under which the difference between the two is negligible have been refined. It was found that the difference in buckling pressures is insignificant (less than 5 %) for length-to-radius ratios greater than 1.0. Additionally, two simplified formulas from the dozen compared were identified as particularly reliable, yielding accurate results across a wide range of shell geometries. The study further revealed that the discrepancy between theoretical and experimental buckling stresses increases as the length-to-radius ratio decreases, with the effect becoming particularly pronounced for short shells with length-to-radius ratios below 1.0. Finally, the study summarizes key aspects related to the stability of circular cylindrical shells, including imperfection sensitivity, lower bound estimates, and stiffener requirements.
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