The paper describes experimental tests carried out on three ring-stiffened circular conical shells that suffered plastic general instability under uniform external pressure. The cones were carefully machined from EN1A mild steel to a very high degree of precision. The end diameters of the cones, together with their thicknesses were the same, but the size of their ring stiffeners was different for each of the three vessels. In the general instability mode of collapse, the entire ring-shell combination buckles bodily in its flank. The paper also provides three design charts using the results obtained from these three vessels, together with the results obtained for twelve other vessels from other tests. All 15 vessels failed by general instability. One of these design charts was based on conical shell theory and two of the design charts were based on the general instability of ring-stiffened circular cylindrical shells, using Kendrick’s theory, which were made equivalent to ring-stiffened circular conical shells suffering from general instability under uniform external pressure. The design charts allowed the possibility of obtaining plastic knockdown factors, so that the theoretical elastic buckling pressures, for perfect vessels, could be divided by the appropriate plastic knockdown factor, to give the predicted buckling pressure. The theoretical work is based on the solutions of Kendrick, together with the finite element program of Ross, namely RCONEBUR and the commercial finite element package ANSYS. This method can also be used for the design of full-scale vessels.