This article addresses the issue of reproducing quantitative pressure-drop predictions for constant shear-viscosity fluids in contraction and contraction/expansion flow geometries. Experimental observations on pressure-drop for severe strain-hardening Boger fluids reveal significant enhancement above Newtonian fluids in axisymmetric but not planar configurations. This discrepancy has eluded predictive capability to date in contraction flows when utilising Oldroyd models. Here, we identify why this is so. The 4:1:4 contraction/expansion flow and adjustment of material parameters provides the key to resolving this dilemma in comparative form to the 4:1 counterpart problem. During the investigation, Oldroyd-B fluid compositions of various solvent: polymeric viscosity ratio splits are employed. A hybrid finite element/volume algorithm of incremental pressure-correction time-stepping structure is utilised, reflecting some novel features with respect to the discrete treatment of pressure. (c) 2008 Elsevier B.V. All rights reserved.