This paper describes the isothermal die swell using our recent quasi-1D model for fast (high Deborah number) contraction flows of polymers melts. Because the model analyzes the flow in several flow regions as one continuous process, it makes possible to evaluate the die swell as a qusi-1D extrudate flow in dies of various lengths. Using the asymptotic matching condition for the change in flow type at the die exit allowed us to find the swelling profile for extrudate along the flow direction. The calculations in paper 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 swelling model involves no fitting parameter and is applicable for calculations using any viscoelastic constitutive equation.