This paper is concerned with the comparison of the results of numerical simulation of confined flow past a cylinder to birefringence data for two polymer melts. The Phan-Thien and Tanner (PTT) constitutive equation and the Rivlin-Sawyers (RS) constitutive equation with the Papanastasiou, Scriven, and Macosko (PSM) damping function were each fit to the shear viscosity and extensional viscosity data of both linear low-density polyethylene (LLDPE) and low-density polyethylene (LDPE) melts to determine the values of the model parameters. Finite element calculations were carried out using the 4 x 4SUPG and 4 x 4SU methods for the PTT model and the method developed by Dupont, Marchal, and Crochet for the RS model. Isochromatic birefringence patterns calculated from the predicted stress field and the stress-optic law were compared to birefringence data. Good agreement was found between the birefringence data and the numerical predictions, except in the immediate vicinity of the cylinder surface. Large extensional stresses were observed and predicted along the centerline downstream of the cylinder for LDPE. This behavior was not observed or predicted for LLDPE. Stress fields obtained from birefringence measurements for LDPE flowing past three cylinders in a channel indicate an effect of deformation history on the flow behavior of LDPE. It is shown that the PTT model does not correctly predict the rheological behavior of LDPE as a function of shear history because the time scale of structural recovery is much longer than the relaxation time associated with viscoelasticity.