This paper investigates local elastic buckling of thin long cylindrical shells under external pressure. Based on Donnell's and Sanders’ theories of thin shells and von Karman nonlinearity assumptions, the potential energy is derived. The buckling load and curves of the static equilibrium path are obtained using the Ritz method. The results are validated with the existing ones in the literature. Furthermore, the case where the pressure is perpendicular to the deformed state is compared with a dead loading. It is demonstrated that the former yields a lower critical pressure in both shell theories. © 2017 Elsevier Ltd