Consideration is given to the influence of elongational properties on flow characteristics in the case of shear-thinning highly elastic fluids in an abrupt contraction. Sufficient data has been published to demonstrate that viscoelasticity can have a significant effect on flow characteristics in abrupt contractions. This paper reports on numerical experiments with four representative test-fluids of Phan-Thien-Tanner models. Furthermore, a new dimensionless number that takes into account elongational properties is proposed. Of major importance is the observation that the vortex enhancement and the energy loss in the entrance region both vary strongly with the elongational properties of Phan-Thien-Tanner models. Numerical results are qualitatively in good agreement with experimental measurements on polymer solutions and melts. Finally, this numerical study provides a fundamental basis, which may be quite useful for the prediction of viscoelastic fluid flows by using numerical modeling, and for the calculation of rheometrical properties of viscoelastic fluids through constitutive equation parameter adjustment.