A finite element analysis was carried out for a 4:1 planar contraction die for polymer melts using the viscoelastic constitutive equation of Leonov. Viscoelastic fluids showed significant differences in pressure drop and birefringence in contraction and expansion flows. The pressure drop was higher and the birefringence smaller in expansion than in contraction flow. The difference increased with increasing flow rate. The nonlinear Leonov model was shown to describe the viscoelastic effects observed in experiments.