A comparative study of the performance of several constitutive models in describing the behaviour of a solution of polyisobutylene in a mixed dekalin/polybutene oil solvent (fluid S1) in simple and complex flows is presented. Four different models were used, two each of the integral and differential type. The former are modifications to the well-known Wagner model, where it is assumed that the damping function parameters are allowed to vary for each relaxation mode. The latter include the Giesekus and PTT models; in the case of the PTT the slip coefficient is allowed to vary with the second invariant of the rate-of-deformation tensor. This form of the PTT model provides the best description of the behaviour of the fluid in simple flows, followed by the generalised PSM, generalised Wagner and Giesekus. The PTT and generalised PSM models were then used, in conjunction with the well-known Binding analysis for contraction flows, in order to predict the entry pressure drop in axisymmetric flows with contraction ratios in excess of 20 : 1. Of the three observed flow regimes, two are accurately predicted by the analysis, while an (expected) overestimation is observed for the third one. Once again, the PTT model yields the best results. These strongly suggest that, from the transition from the second to the third regime onwards, the entry pressure drop is dominated by extensional effects, the fluid elasticity playing only a minor role.