The necessary condition for the multiplicity in deformation rate was given by Hill. The condition is ΔεuΔsu=0, where su denotes the nominal stress rate, and Δ shows the difference between any two multiple solutions. However, many proposed criteria of plastic instability in published literature did not take into consideration this necessary condition. They were based on phenomenological aspects. The sufficient condition for the multiplicity is deduced from the requirement which makes the equivalent strain rate εs indefinite. This is given by εuεu=0, which is called Z-plane in su space. Plastic instability or unloading from a stable state always occurs on Z-plane. With respect to the formability in metal forming, especially, the possibility of plastic instability, processes are examined in plane stress, plane strain and three dimensional conditions. In sheet forming alternative cniterion, s1=0 is also proposed for positive γ which is defined by the ratio ε2/ε1. In bulk forming, the dependency of ductility upon mean normal stress is discussed, and the decrease of ductility is shown with increasing the mean stress. Furthermore, the occurrence of shear banding and its mode are studied. Since the shape of loading path is normally monotonic in su space, a loading path intersects Z-plane only once and then plastic instability also can occur only once. Therefore, localized necking, in general, is merely the plastic deformation confined into a very thin layer with a rigid region on its both sides.