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Conical shells are often joined to cylindrical shells and under internal pressure, the intersection between the large end of a cone and a cylinder is subjected to a large circumferential compressive stresses which can lead to its failure by whether axi-symmetric gross plastic deformation involving excessive inward deformations or non-symmetric buckling which accompanies by circumferential waves around the intersection. In Pressure Vessel Design by Analysis, the designer is required to address both these behavior modes when specifying the allowable static load. In this paper, plastic collapse or gross plastic deformation load is evaluated for a typical pressure vessel with conical head using plastic work curvature criterion and the results are compared with other criteria suggested by international standards such as ASME. The plastic work curvature criterion is based on the plastic work dissipated in the structure as loading progresses and may be used for structures subject to a single load or a combination of multiple loads. The results of analyzing using this new criterion show that the plastic collapse load given by the plastic work curvature criterion is robust and consistent and is in the close agreement with the results from international codes. The most significant aspect of the proposed method in which plastic work curvature criterion has been used is that the plastic collapse loads are determined purely by the inelastic response of the structure and therefore they are not influenced by the initial elastic response: a problem with some other established plastic criteria. The results also show that the design load is mostly limited by the formation of an axi-symmetric gross plastic deformation in the intersection of the vessel prior to the formation of non-symmetric buckling modes