The relation between the stress relaxation in step shear strain test and the extrudate swelling behavior of viscoelastic fluid was investigated by using finite element method to simulate the extrudate swell of the IUPAC-LDPE melt through a long circular die. Four separable KBKZ-type integral constitutive equations depicting different stress relaxation characteristics in step shear strain test were used in the simulations, including the Wagner model, the Osaki model, the PSM model, and a new three-parameter rational type model developed by the authors. Our numerical results were validated by comparing with the previous predictions of swell ratio for the PSM model. It is noted here that the stress relaxation characteristic at large strains in step shear strain test has a significant influence on the numerical prediction of swell ratio of the IUPAC-LDPE melt, especially at high shear rate. The effect of the stress relaxation characteristics on the exit pressure drop is also presented. (c) 2006 Elsevier B.V. All rights reserved.