The poor solutions of numerical simulations at a contraction has often been attributed to the numerical scheme used. However, the solution of a numerical simulation is also highly dependent on the constitutive equation. A study of various constitutive equations on the simulation of the 4 : 1 contraction flow is made in this paper, and their effects on the results analyzed. The constitutive models considered include the Upper Convected Maxwell model, the Oldroyd-B model, the White-Metzner model, the Phan-Thien-Tanner model and the Giesekus-Leonov model. It was found that although the Phan-Thien-Tanner model gave the best results,the solution at higher shear rates were still not satisfactory.