Numerical simulations of axisymmetric extrudate swell for a low density polyethyrene (LDPE IUPAC-A) melt were carried out using the K-BKZ model as an integral type and the PTT and Larson models as a differential type. We employed both the reversible and irreversible models for the K-BKZ and Larson models to investigate the effect of reversing deformation on the extrudate swell from a straight die. First, relaxation spectrum and nonlinear parameters in the constitutive equation were determined from dynamic data of linear viscoelasticity and steady shear flow data by using the nonlinear regression, and then they were applied to the simulation of extrudate swell problem. We evaluated the applicability of these models by comparing experiments and simulation for both rheological data and extrudate swell ratio. For the K-BKZ model, the reversible model over-estimates the swell ratio in high shear rate, whereas the irreversible model predicts the experimental data with high accuracy. The irreversible Larson model also shows the good prediction of swell, on the other hand, the reversible one over-estimates the swell and there exists the multiple solutions.For the PTT model, we carried out the simulation using the models with different values of nonlinear parameter, ε , which has the same steady shear flow properties and the different properties of stress relaxation under reversing double step deformation. The model having the larger stress in the stress relaxation under reversing double step deformation shows the larger swell. From these results, we find that the consideration of reversing deformation characteristics is required for the extrudate swell from the straight die.