In this study, three nonlinear rheological models consisting of the Giesekus, the FENE-P, and the Phan-Thien-Tanner model are used to simulate the flow of a viscoelastic fluid through a planar 4:1 contraction. Both stress and velocity fields are examined at different sections of the flow and the predictions of the numerical simulations are compared with the experimental results of L.M. Quinzani, R.C. Armstrong and R.A. Brown, J. Non-Newtonian Fluid Mech., 52 (1994) 1-36. Overall, the numerical simulations allow a description of the essential features of the flow, and reproduce much of the experimental results with good accuracy. Excellent qualitative agreement between the numerical results and the experimental observations is reported. However, the agreement remains semi-quantitative especially for the first normal stress difference around the entry section of the flow. This is to be expected in view that the simulations were limited to only one-mode models.