Lightweight thin-walled cylindrical shells subjected to external loads are prone to buckling rather than strength failure. The buckling of an axially compressed shell is studied using analytical, numerical and semi-empirical models. An analytical model is developed using the classical shell small deflection theory. A semi-empirical model is obtained by employing experimental correction factors based on the available test data in the theoretical model. Numerical model is built using ANSYS finite element analysis code for the same shell. The comparison reveals that the analytical and numerical linear model results match closely with each other but are higher than the empirical values. To investigate this discrepancy, non-linear buckling analyses with large deflection effect and geometric imperfections are carried out. These analyses show that the effects of non-linearity and geometric imperfections are responsible for the mismatch between theoretical and experimental results. The effect of shell thickness, radius and length variation on buckling load and buckling mode has also been studied. Copyright © 2009 John Wiley & Sons, Ltd.