Abstract: A new valid method of stress categorization- “primary-least structure method”(PLSM) is proposed. The method is based on the stress-linearized technique and elastic finite element analyses (FEA). During the classification, the primary stresses (Pm + Pb) are evaluated in the “primary least structure”, while other stresses (PL+Q+F) in the original structure. By removing the “ruinous constrains” from the original structure, the lower primary stress is extracted, from which the greater allowable pressure approaching the lower-bound limit load can be obtained. An example is presented to demonstrate the application of the “primary-least structure” method as a stress categorization tool. The result shows that a higher allowable pressure can be obtained by this method, compared with the procedure without stress-linearized technique and the approach given by present Code.