The flow of a 5.0 wt.% solution of polyisobutylene in tetradecane through a planar 4 : 1 contraction exhibiting a shear thinning viscosity is simulated using the flow-type sensitive quasi-Newtonian fluid model. The shear viscosity is fitted by the Giesekus model, which, with the chosen parameters, leads to an extension thickening elongational viscosity. The stress and velocity fields of the numerical simulations are compared with the experimental results of Quinzani et al. [J. Non-Newtonian Fluid Mech. 52 (1994) 1-36] and the numerical results of the viscoelastic simulation using the Giesekus model of Azaiez et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 253-277]. It can be shown that the quasi-Newtonian fluid qualitatively predicts the essential features of the flow in the vicinity of the contraction.