In this paper, the condition for strain localization bifurcation is studied using Lagrangian description. The localization criterion with respect to the reference con®guration is obtained by relating the rate of the second Piola-Kirchoff stress to the rate of Cauchy-Green deformation tensor. When transferred to the present con®guration, it is equivalent to the one which is obtained when Truesdell rate of Cauchy stress is used in the rate problem. An example for the localization response for a set of triaxial extensions is presented using a speci®c ®nite-deformation thermo-elastic-plastic model.When a small-deformation based localization criterion is used, i.e. when some terms in the localization criterion are neglected, the localization response, at some loading paths, becomes signi®cantly different from that obtained in the presence of these terms. It is therefore concluded that ®nite deformation tools should be employed when localization analysis is performed even when the small deformation hypothesis is otherwise considered as valid.
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