This paper develops an isothermal quasi-1D model for fast (high Deborah number) contraction flows of polymers from a reservoir to a die of circular or rectangular cross-sections. Two components of composite flow models, inhomogeneous elongation and a modified unsteady shearing. employed in different regions of the full flow domain are connected in succession with the use of asymptotic matching boundary conditions. The model. based on a stable and descriptive set of viscoelastic constitutive equations, demonstrates a reasonable good agreement with experimental and direct numerical data with no adjustable parameters. It employs easy PC numerical calculations. The predictions of the model are improved for contraction flows with higher values of Deborah/Weissenberg number and contraction ratio. (C) 2004 Elsevier B.V. All rights reserved.