Flow of a shear thinning, moderately concentrated solution of monodisperse high molecular weight polystyrene has been studied in a nonhomogeneous axisymmetric stagnation flow. Shear and extensional rheometry have been used to characterize the rheology of the solution. Multimode Giesekus and Phan-Thien-Tanner (PTT) models, and a single mode PTT model with a White-Metzner rate dependent relaxation time (PTT-WM) were fit to the rheological data. Transient uniaxial elongational measurements show significant extension hardening, which could only be predicted by the PTT model. The Giesekus model provided the best representation of shear flow data, but substantially underpredicted the measured extensional viscosity. Flow birefringence was used to measure integrated axisymmetric shear and normal stress profiles as a function of position. These measurements were compared with the results of numerical simulations, performed using an adaptive finite element technique, with the three constitutive models. The computed results with the 3-mode Giesekus model accurately portrayed experimental shear and normal stresses in both forward and rear stagnation flow up to Weissenberg numbers (We) of O(1). At higher We, the Giesekus model underpredicts normal stresses in the rear stagnation flow, where elongational gradients dominate. Both PTT and PTT-WM models gave rise to unrealistically large extensional stresses in the rear stagnation flow even at moderate We which led to poor agreement with experimental data. On the basis of these comparisons, it appears that the elongational properties of the solution are intermediate between the Giesekus and PTT, but much closer to the Giesekus, predictions. This is in conflict with the experimentally measured uniaxial viscosity, which suggests that the PTT model should be superior in flows with significant uniaxial extension.