The parallel large-scale unstructured finite volume method proposed in [Sahin, A stable unstructured finite volume method for parallel large-scale viscoelastic fluid flow calculations, J. Non-Newtonian Fluid Mech. 166 (2011) 779-791] has been applied to investigate the three-dimensional creeping flow of an Oldroyd-B fluid past a confined circular cylinder in a rectangular channel at relatively high Weissenberg numbers. The numerical method is based on side-centered finite volume method where the velocity vector components are defined at the mid-point of each cell face, while the pressure term and the extra stress tensor are defined at element centroids. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance the pressure-velocity-stress coupling. The combination of the present numerical method with the log-conformation representation proposed in [R. Fattal, R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281-285] and the geometric non-nested multilevel preconditioner for the Stokes system have enabled us to simulate large-scale viscoelastic fluid flow problems on highly parallel machines. The calculations are presented for an Oldroyd-B fluid past a confined circular cylinder in a rectangular channel at relatively high Weissenberg numbers and compared to those obtained for Newtonian fluids. The present numerical calculations reveal three-dimensional purely-elastic instabilities in the wake of a confined single cylinder which is in accord with the earlier experimental results in the literature. In addition, the flow field is found out to be no longer symmetric in the wake of the cylinder at high Weissenberg numbers. (C) 2012 Elsevier B.V. All rights reserved.