AbstractWhen stretched under uniaxial stress, ductile polymers usually exhibit unstable plastic deformation, which embodies two phases: (a) yielding with the formation of a neck and (b) cold‐drawing with the propagation of necking shoulders. The mechanical state associated with this deformation behavior is analyzed. The discussion is divided into three parts. The first part is a general treatment of the constitutive function of flow stress in the plastic state, in which a series of relations among various characterizing parameters are formulated. The second part provides three mechanical criteria for necking deformation and propagation of necking shoulders: the condition of unstable plastic deformation requiring \documentclass{article}\pagestyle{empty}\begin{document}$ D_P = - \left( {\partial {{\ln \dot \varepsilon } \mathord{\left/ {\vphantom {{\ln \dot \varepsilon } {\partial \varepsilon }}} \right. \kern-\nulldelimiterspace} {\partial \varepsilon }}} \right)_P < 0 $\end{document} the stabilizing deformation mode, which requires \documentclass{article}\pagestyle{empty}\begin{document}$ \gamma _p = \left( {{{dD_p } \mathord{\left/ {\vphantom {{dD_p } {d\varepsilon }}} \right. \kern-\nulldelimiterspace} {d\varepsilon }}} \right)_P > 0 $\end{document} and the obvious localization of unstable plastic deformation. The third part describes a mathematical model which can be used in calculations to fit the contour of the necking shoulder. This model is developed according to rational considerations for the relation of In \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document} to ε. Experimental data on PE rod specimens are well fitted by this model. © 1993 John Wiley & Sons, Inc.