We calculated the annular extrudate swell of a polymer melt passing through the rotating-tip tubing die proposed by Gupta et al. (Ref. Int. Polym. Process., 14, 51 (1999)) by the finite element method. The multiple-mode Phan-Thien Tanner (PTT) model was employed as a constitutive equation for a viscoelastic fluid. We changed the rotation speed of the rotating-tip tubing die and the die geometry having straight, converging and diverging flow region. Results obtained are follows. (1) When the rotation speed of the rotating-tip increases, the annular extrudate swells toward the center axis. And the diameter of an extrudate decreases with an increase of the rotation speed of the rotating-tip. (2) The difference of die geometries has an influence on the shape of an extrudate. (3) In case of low flow rate, the geometry of annular extrudate would be independent of the die geometry at a high rotation speed of the rotating-tip.