An analysis is developed to account for the effects of imperfections on the collapse strength of spherical shells. The analysis is empirical but is based on an engineering evaluation of recent tests of near-perfect deep spherical shells and spherical caps. Sixty-two models were machined with local thin spots and flat spots and subjected to external hydrostatic pressure. The analysis is in good agreement with experimental results despite the severity of imperfections selected to test the analysis. The limitations of the analysis are discussed and curves showing the relationship between out of roundness and local radius are presented to aid the design engineer in establishing acceptable tolerance limits for fabrication of spherical shells.