Further numerical simulations have been undertaken for the creeping flow of a well-characterized polymer solution (fluid S1) in entry flow of a 24:1 axisymmetric contraction. The fluid has been modeled using an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times. New results are obtained for the experiments previously performed by Maia [J. Non-Newtonian Fluid Mech. 85 (1999) 107]. The numerical solutions show that the vortex kinematics in the reservoir is captured well, showing a great vortex activity in agreement with the experiments. The numerically obtained pressure drops are also in agreement with the experiments up to the point of the onset of flow instabilities observed experimentally. (C) 2001 Elsevier Science B.V. All rights reserved.