It is very important to predict the collapse strength of externally pressurized spherical shell which have imperfections such as welding deformation and residual stresses. Many experimental studies on this problem have been made by M. Krenzke et al., but few theoretical researches have been reported. To exactly obtain a numerical solution of the collapse pressure of the spherical shell, it is necessary to consider the strain hardening in the elasto-plastic analysis of the axisymmetric shell. This paper introduces a newly developed method by which the elasto-plastic behavior of the axisymmetric shell can be exactly expressed by using the membrane forces and bending moments, and moreover investigates effects of the imperfections on the collapse pressure of the spherical shell. Main conclusions obtained from this study are as follows ; (1) The usefullness and accuracy of the new method are confirmed by comparison with the experimental results. (2) The more plastically the spherical shell collapses, the smaller the effects of the imperfections on the collapse pressure becomes. (3) In the case that a penetrator or a partial sphere is welded circumferentially to the spherical shell, according as the diameter of the penetrator or partial sphere increases, the collapse pressure of the spherical shell will increase if both have same value imperfection by welding. (4) If the spherical shell has the residual stress, its collapse pressure will reduce.