The paper reviews the theoretical analysis for determining the pressure contained by a thick-walled closed-ended cylinder at the onset of yielding and during the subsequent plastic deformation up to the maximum or "ultimate" pressure which the cylinder will withstand. The analysis requires shear stress-strain data which can be derived from either torsion or tension tests. The derivation of shear stress-strain data from torsion tests on solid or tubular specimens is considered. It is shown that if this analysis is applied to the results published by Marin and Weng there is good agreement between the shear stress-strain curves derived from solid or tubular specimens. Additional experimental information is given on torsion tests on solid and tubular specimens, which further confirms the proposed analysis. Some further tests on torsion specimens of different sizes show that though there is some size effect on the initial yield of mild steel, there is no significant size effect at large strains. The analysis of tension results to obtain the necessary tensile stress-strain data is also considered, and it is noted that for the calculation of the ultimate pressure data is required for strains in excess of the strain at the onset of necking in tension. Consequently it is not reasonable to base the tensile stress on the original area or indeed the area of the neck, and it is necessary to consider the "true stress" at the neck, which has been analyzed by Bridgman. The results of bursting tests are considered in relation to values predicted for torsion and tension data, and the advantages and disadvantages of each are considered. It is concluded that torsion test data is to be preferred for many reasons.