The allowable plastic load in pressure vessel design by analysis is determined by applying a graphical construction to a characteristic load-deformation plot of the collapse behavior of the vessel. This paper presents an alternative approach to the problem. The plastic response is characterized by considering the curvature of a plot of plastic work dissipated in the vessel against the applied load. It is proposed that salient points of curvature correspond to critical stages in the evolution of the gross plastic deformation mechanism. In the proposed plastic work curvature (PWC) criterion of plastic collapse, the plastic load is defined as the load corresponding to zero or minimal plastic work curvature after yielding and the formation of plastic mechanisms have occurred. Application of the proposed criterion is illustrated by considering the elastic-plastic response of a simple cantilever beam in bending and a complex three-dimensional finite element analysis of a nozzle intersection. The results show that the proposed approach gives higher values of plastic load than alternative criteria when the material exhibits strain hardening. It is proposed that this is because the PWC criterion more fully represents the constraining effect of material strain hardening on the spread of plastic deformation.