This paper discusses the numerical modeling of capillary break-up extensional rheometer procedures (CaBER) using Arbitrary Lagrangian/Eulerian (ALE) methods. Different models, fluid viscosities and aspect-ratios are studied, employing a hybrid finite element/finite volume spatial approach. 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. The results are validated against equivalent experimental results from the literature. By employing various constitutive models, viscoelastic response has been studied for some strain-hardening fluids. Two different polymeric to solvent viscosity ratios are studied covering both high and low solvent fractions. The relaxation time and the apparent extensional viscosity are calculated for both viscosity ratios, from the evolution of the mid-filament diameter. For these viscoelastic solutions, the extensional viscosity increases with strain, and this trend, and its range of values in apparent extensional viscosity values agree well with the literature. Also, estimated relaxation times are found to lie in close agreement with the actual relaxation time data used for the fluids in question. (c) 2007 Elsevier B.V. All rights reserved.