Annular extrudate swell is studied for a fluoropolymer (FEP) melt using a tubular die. The theological data of the melt have been fitted using (i) a viscous model (Cross) and (ii) a viscoelastic one (the Kaye - Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko or K-BKZ/PSM model). Numerical simulations have been undertaken to study the extrudate swell of the FEP melt in an annular die. Compressibility. thermal and pressure effects on viscosity, and slip at the wall were taken into account. In all cases, slip at the wall is the dominant contribution reducing the swelling when compared with corresponding no-slip simulations. The viscous (Cross) simulations show that the swell decreases with increasing apparent shear rate, which is opposite to what happens in the extrusion of viscoelastic melts. On the other hand, the viscoelastic (K-BKZ) simulations correctly obtain increasing swelling with increasing shear (flow) rates. It was found that due to the mild visco-elasticity of FEP and its severe slip at the wall the swelling of this melt is relatively small, reaching values of about 20% for a wide range of apparent shear rates, exceeding 5 000 s(-1). This is corroborated by experimental observations.