Much of the available literature on the flow of non-Newtonian fluids through abrupt contractions concentrates on the use of differential or integral models of viscoelastic behaviour in order to attempt to predict the flow pattern, and in particular, the effect of elasticity on the development of vortices upstream of the contraction. However, in such flows the dominant influence on the fluid is undoubtedly the rapid extension experienced in passing through the contraction. In such circumstances, memory effects are likely to be less important than strain-thickening, In this paper, we investigate the merits of a simple constitutive model which isolates extensional effects, and shows that essential features observed experimentally can be predicted by such a model for two quite different polymer solutions. The sharpness of the re-entrant corner is shown to be a determining factor. For an abrupt corner, a vortex pattern forms upstream of the contraction as the flowrate is increased. This does not appear until higher flowrates, if the corner is rounded. The presence or otherwise of inertia also has a significant influence on the way in which the vortices develop, giving rise in some cases to a so-called lip-vortex mechanism and in others to a corner-vortex mechanism.