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Highlights • Numerical study of different cone geometries with semi-vertex angle ß = 10°…75°. • New improved shell buckling design factors for conical shells in form of a simple analytic equation. • Different equivalent cylinder approaches investigated. • Imperfection sensitivity of Interstage ½ of Vega launch-system analyzed. Abstract Thin-walled conical shells are used as adapters between cylindrical shells of different diameters in launch-vehicle systems. Conical shells carry heavy payloads and are consequently subjected to axial compression. The buckling load of these shells is very sensitive to imperfections (geometry, loading conditions) which results in a critical disagreement between theoretical and experimental results for axially loaded conical shells. The design of these stability critical shells is based on classical buckling loads obtained by a linear analysis which are corrected by a single knockdown factor (0.33 - NASA SP-8019) for all cone geometries. This practice is well established among designers and hasn't changed for the past 50 years because the buckling behavior is till today not very well understood. Within this paper an analytical and numerical lower-bound procedure for conical shells under axial compression is proposed. Data of previous experimental testing campaigns are used to validate the new design criteria for different conical shell geometry configurations. The whole design concept is demonstrated by means of the Interstage 1/2 of the Vega launcher and it is concluded that a revision of the current design recommendation for conical shell structures may results in a significant weight reduction potential. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]