We present in this work a model of flow iduced crystallization. In a former work [A. Poitou, A. Ammar, Polymer crystallization induced by strain or flow: a thermodynamic approach, C. R. Acad. Sci. Me´canique (Janvier 2001) 5-11] we showed how the thermodynamic formalism of the standard materials could be applied to the crystallization of a polymer with a viscous behavior. We described within this framework the coupling between the mechanical behavior and the phase transition. The difficulty raised in this paper relates to the writing of the viscoelastic behavior within the thermodynamic framework. A molecular vision of the Maxwell model is used. Within this framework, the equation of flow induced crystallization expresses naturally the influence of the mechanical sollicitation on the kinetics. This equation can be applied to simulate complex sollicitations without limitation to the case of the simple elongation or the simple shearing. We compare finally the results of simulations with an experimental case of plane elongation [M. Vigny, A. Aubert, J.M. Hiver, M. Aboulfaraj, C. G'Sell, Constitutive viscoplastic behaviour of amorphous pet during plane-strain tensile stretching, Polymer Engrg. Sci. 39 (12) (December 1999) 2366]. © 2002 E´ditions scientifiques et me´dicales Elsevier SAS. All rights reserved.