Abstract Multi-crystal metals have the property of volume conservation in the plastic state. In the infinitesimal deformation plas-ticity the strain tensor can be split into a deviator part and a volumetric part. The vanishing of the first variant of the strain tensor is equiv-alent to the volume conservation. Furthermore, the split of the strain into an elastic part and a plastic part is also adopted widely. The flowrule is thus established. These two splits are not confirmed in the finite deformation plasticity. The plasticity criterion and the flow rule arethus facing great challenge. There are various definitions of strain measures in the finite deformation theory. Though the choosing of strainmeasure is arbitrary in the elastic problem, it is strongly restricted in the plastic problem. By theoretical and experimental studies, it isshown that the logarithmic strain is the only suitable strain measure in the metal forming problem. Abstract Multi-crystal metals have the property of volume conservation in the plastic state. In the infinitesimal deformation plas-ticity the strain tensor can be split into a deviator part and a volumetric part. The vanishing of the first variant of the strain tensor is equiv -alent to the volume conservation. Furthermore, the split of the strain into an elastic part and a plastic part is also established widely. The flowrule is thus established. Both plastic parts are not recognized in the finite deformation plasticity. The plasticity criterion and the There are various definitions of strain measures in the finite deformation theory. Though the choice of strain measures in arbitrary elastic problem, it is strongly restricted in the plastic problem. the logarithmic strain is the only suitable strain measure in the metal forming problem.