A method for measuring the elongational viscosity of polymer melts and solutions has been generalized and evaluated by means of numerical simulations. The method involves passing a material through a cylindrical, converging die whose semihyperbolic shape mandates a shear-free, or nearly shear-free, flow within the die, assuming wall slip. From the analysis of the relevant flow equations in the die, an expression for elongational viscosity is derived under less restrictive conditions than in previous studies. This expression consists of two terms, one of which is a measurable effective elongational viscosity defined in terms of the change in pressure over the die, the volumetric flow rate and the Hencky strain determined by the geometry. To evaluate this method, finite element techniques are used to calculate the flow of a low-density polyethylene melt in two semihyperbolically converging dies. After confirming that purely elongational flow is produced within the die, assuming wall slip, the effective elongational viscosity is computed from the calculated flow field and these values are compared with the values of elongational viscosity found by integrating the constitutive equation for the material in elongational flow. Over the wide range of elongation rates considered, very good agreement is found between these two sets of values when the time associated with the effective viscosity is appropriately specified. Further, a similar analysis for a Newtonian fluid showed that the effective elongational viscosity satisfies the Trouton ratio over the range of elongation rates considered. These results indicate that the measured effective elongational viscosity is an excellent approximation to the material's true elongational viscosity. Consequently, semihyperbolically converging dies can be used effectively to obtain transient elongational viscosity measurements at constant strain or constant strain rate. (C) 2003 Elsevier B.V. All rights reserved.