The paper begins with derivation of true stress–true strain data, including postnecking section. Available results of past uni-axial tests on round 10 mm diameter and 200 mm long mild steel samples are the basis of the conversion. The steel in question was used to manufacture ten torispherical domes that were in the past tested for burst. Hence, the relevance of matching material model is necessary for the finite elements (FE), analyses. In the past, plastic instability and constraints on the magnitude of plastic strains were postulated as criteria for the burst of internally pressurized torispheres. These criteria for burst pressure are being examined and benchmarked against the tests. The current paper, using the FE analyses, shows that modification of constraints on plastic strains has only marginal effect on the burst which still remains on the unsafe side of test data by a sizeable margin. The same is found to be true for plastic instability criterion. Subsequent computations moved back to the use of engineering stress–strain. Then, two types of computing are carried out here, based on multisegment and bilinear modeling of material. Computed results of burst pressure follow the test data to within (−6%, +10%). These results are far better than all the previous.