The stress evaluation by elastic analyses for protection against plastic collapse in Appendix 9 is based on maximum shear stress theory (Tresca theory). On the other hand, the stress evaluation by elastic-plastic analysis and design equations by flow stress for design pressure for cylindrical shell and spherical shell in KD-221 is based on distortion energy yield stress theory (von Mises theory). With regard to materials with low and intermediate Sy/Su, in particular the primary stress evaluation based on Tresca stress for elastic analysis in current Div.3 is much more conservative than that based on flow stress equations similar to elastic-plastic analysis from experimental results. In Section VIII Div.2, von Mises yield criterion is used for stress evaluation for elastic analysis because it matches experimental results more closely than Tresca yielding criterion and is also consistent with plasticity algorithms used in elastic-plastic analysis. Therefore in Div.3 von Mises stress should be used for elastic analysis in the same way as in Sec. VIII Div.2. For materials with high Sy/Su, the primary stress evaluation based on von Mises criterion for elastic analysis is less conservative than that based on flow stress equations similar to elastic-plastic analysis because of a difference in design factor of 1.5 for elastic analysis and 1.732 for flow stress equations. Therefore, we propose using von Mises criterion for protection against plastic collapse with design correction factor using Sy/Su in Appendix 9 in order to remove excessive conservativeness for materials with low and intermediate Sy/Su. The validity of this proposal is shown in this paper.