This article describes isothermal contraction flows and extrudate swell, using our recent model for fast (high Deborah number) contraction flows of polymers melts. The model analyzes the polymer flow in several regions as one continuous process. This approach makes possible to evaluate the extrudate swell as a result of complex contraction polymer flow in dies of various length. Using the asymptotic matching conditions for the change in flow type at the die exit allowed us to calculate the swelling profile for extrudate in the flow direction. The present calculations performed using a multi-mode viscoelastic constitutive equation of differential type, are compared with the experimental/direct numerical data including basic rheological tests. The presented complex model for contraction flow and swelling consists of no fitting parameter and is applicable for calculations using any viscoelastic constitutive equation. POLYM. ENG. SCI., 48:2340-2353, 2008. (C) 2008 Society of Plastics Engineers