Experimental buckling pressures are given in the paper for six cylinder-cone combinations which were carefully machined and stress-relieved and then tested under uniform external pressure. Failure in all cases occurred by asymmetric buckling (i.e. with circumferential waves); although some failures were elastic, others were elastic-plastic. Theoretical buckling pressures for the models (assumed perfect) were obtained from a variational finite-difference formulation of the problem which has been incorporated into a comprehensive digital computer program.