The extrudate swell phenomenon of a high-molecular-weight HDPE is modelled using the following viscoelastic constitutive equations: the multi-mode KayeBernstein-Kearsley-Zapas (K-BKZ) integral model with the Wagner and the Papanastasiou-Scriven-Macosko (PSM) damping functions, and multi-mode Phan-ThienTanner (PTT), Giesekus and Double Convected Pom-Pom (DCPP) differential models. The high-molecular-weight high density polyethylene (HDPE) is rheologically characterized and the experimental data have been used to fit the parameters of the constitutive models. Experimental results on extrudate swell are compared with the numerical predictions. The simulation results showed that the integral K-BKZ model highly overpredicts and the differential PTT, Giesekus and DCPP models slightly under-predict the experimental measurements. When the capillary reservoir is excluded from the simulations, the predictions of the integral models are significantly reduced close to the experimental data, while those of the differential models remain practically unaffected. Although both integral and differential models used represent the rheological data equally well, an explanation of the dramatically different predictions of extrudate swell by the integral and differential models remains elusive.