This article considers the dynamics of filament stretching for viscoelastic liquids. We investigate the consequences of employing both fe and fv spatial discretisations within an incremental pressure-correction scheme, considering various mesh movement and free-surface tracking techniques. Finite element discretisation is employed for the momentum and continuity equation, whilst a pure-upwinding cell-vertex finite volume representation is utilised for the hyperbolic stress equation. Compressive mesh procedures outperform volume-of-fluid counterparts, and when coupled to an ALE-formulation governing mesh movement, provide a powerful technique to access impressively large Hencky-strains. If precision in determination of free-surface curvature is demanded, a particle-tracking approach is shown to be preferable to a kinematic condition for surface-level. Results of the study lie in close agreement with the literature in trends and measures of Trouton ratio, minimum radius and extensional viscosity predictions. (c) 2006 Elsevier B.V. All rights reserved.