This paper presents an analytical study on the buckling of cylindrical shells with arbitrary circumferential thickness variations under external pressure. Firstly, based on the thin shell theory and separation of variables, corresponding ordinary differential equations of laterally pressured cylinders are obtained. Secondly, the general asymptotic formula of buckling load, which is in terms of thickness variation parameter up to arbitrary order, is derived by combining the perturbation method and Fourier series expansion. Thirdly, the effects of uniform and circumferential modal thickness variations on the buckling of cylindrical shells under external pressure are investigated, respectively, and the results agree well with those available in literature. Particularly, the buckling load reduction of cylinders with circumferential modal thickness variation obtained by the proposed method coincides with the numerical results presented by Gusic et al. This analytical method is applicable for evaluating the stability of laterally pressured cylindrical shells with arbitrary circumferential thickness variations, once the thickness variation is known.