Vortex structure and formation are investigated for both expansion and contraction flows of viscoelastic fluids concentrating on a class of constitutive models due to Phan-Thien and Tanner. Expansion flows are treated in both two and three dimensions, and viscoelasticity is observed to suppress vortex activity. Two-dimensional contraction flows are analysed for highly elastic solutions. Different geometric aspect ratios, levels of inertia and elasticity are considered for these various flows and lip vortices are observed under certain circumstances.