Numerical simulations have been undertaken for the benchmark problem of annular extrudate swell present in pipe extrusion and parison formation in blow molding. The finite element method (FEM) is used to provide numerical results for different inner/outer diameter ratios kappa under steady-state conditions. The Herschel-Bulkley model of viscoplasticity is used with the Papanastasiou regularization, which reduces with appropriate parameter choices to the Bingham-Papanastasiou, power-law and Newtonian models. The present results provide the shape of the extrudate, and in particular the thickness and diameter swells, as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). The pressures from the simulations have been used to compute the excess pressure losses in the system (exit correction). While shear-thinning leads to reduced swelling relative to the Newtonian values for all kappa-values, the opposite is true for shear-thickening fluids, which exhibit considerable swelling. Viscoplasticity leads to decreased extrudate swell as the dimensionless yield stress goes from zero (Newtonian behaviour) to an asymptotic value of fully plastic behaviour. The exit correction decreases to zero with a decrease in the power-law index to zero and an increase in the dimensionless yield stress to its asymptotic limit. However, the decrease is not monotonic: for power-law fluids it has maxima in the range of power-law indices between 0.8 and 0.6, while for viscoplastic fluids it has maxima around Bingham number values of 5. (c) 2006 Elsevier B.V. All rights reserved.