When computational modeling is used to evaluate the true strength of an imperfect elastic-plastic shell structure, the current European standard on shell structures requires that two reference strengths are always determined: the linear bifurcation load and the plastic limit (plastic collapse) load. These two loads are used in more than one way to characterize the strength of all imperfect elastic-plastic systems. Where parametric studies of a problem are being undertaken, it is particularly important that these two loads are accurately defined, since all other strengths will be related to them. For complex problems in shell structures, it is not possible to develop analytical solutions for the plastic collapse strength, and finite element analysis must be used. Unfortunately, because a collapse mechanism often requires the development of very extensive plasticity involving large local strains, and the collapse load is simply at the end of a slowly rising load-deflection curve, it is sometimes difficult for the analyst to accurately determine this plastic collapse strength. This paper describes two methods, based on modifications of the Southwell plot, of obtaining very accurate evaluations of the plastic limit load, irrespective of whether a fairly complete plastic strain field has developed or not. These two methods allow plastic collapse limit loads to be reported with great precision.