In this study, we have used a highly accurate and novel approach to solve numerically for true three-dimensional (3D) viscoelastic flows into sudden contractions. Motivation for this development has been for the advancement of 3D viscoelastic flows in complex geometries, where this new methodology is available as a general solver, written for the open source code OpenFOAM (Weller et al., 1998). The proposed approach is able to include the multiple relaxation times of differential constitutive equations, and has been performed using the Finite Volume Method (RIM), based on a Discrete Elastic Viscous Split Stress (DEVSS) technique (Fortin et al., 1997). In this work, both the Giesekus and Phan-Thien-Tanner (PTT) shear-thinning models were implemented to reproduce flow through a planar 4:1 contraction, where numerical convergence was achieved for a Weissenberg number (We) of 2.9. Direct comparison with experimental data and literature involving 2D and 3D numerical simulations shows this method to be both stable and effective. (C) 2011 Elsevier Ltd. All rights reserved.