The purpose of this report is to propose alternative rules to those given in UG-23(b), UG-28, UG-29, UG-33 and Appendix 1-8 of ASME (1992a) for determining allowable compressive stresses for unstiffened and ring stiffened circular cylinders and cones and unstiffened spherical, ellipsoidal and torispherical heads.The allowable stress equations are based upon theoretical buckling equations which have been reduced by knockdown factors and by plasticity reduction factors which were determined from tests on fabricated shells.The research leading to the development of the allowable stress equations is given in API 2U (1987), Miller (1991), Miller and Saliklis (1993) and the Commentary.