Hitherto the approaches on plastic instability have been carried out m
ainly in evaluating sheet formability. The necking in press forming is
a phenomenon relating to plastic instability. It is classified into d
iffuse and localized neckings. Swift [1] proposed the criterion of dif
fuse necking, and for localized necking Storen and Rice [3] presented
the modified criterion of Hill's [2] in order to make it possible to p
redict the formability in biaxial stretching. Since there is some impe
rfections in these criteria and they do not provide sufficient conditi
ons for the emergence of necking phenomena, they must be improved. Thi
s paper presents comprehensive criteria based on the multiplicity of s
olution.