This study is concerned with the numerical modelling of the Modified Bautista-Manero (MBM) model, for both steady-state and transient solutions in planar 4:1 contraction flow. This model was proposed to represent the structured composition and behaviour of worm-like micellar systems which have importance in industrial oil-reservoir recovery applications. A parameter sensitivity analysis for the rheology of this model is presented in both transient and steady response, covering pure shear and uniaxial extension. In addition, some features in evolutionary flow-structure are demonstrated in contraction flows due to the influence and imposition of start-up transient boundary conditions. The different effects of various model parameter choices are described through transient field response, stress and viscosity fields in the contraction flow setting. Distinction may be drawn between fluid response in the strong/moderate extension hardening regimes by matching both steady-state and transient shear and extensional viscosity peaks, contrasting between micellar (MBM) models against network-based counterparts Phan-Thien/Tanner (PTT). Simulations are performed with a hybrid finite volume/element algorithm. The momentum and continuity equations are solved by a Taylor-Galerkin/pressure-correction finite element method, whilst the constitutive equation is dealt with by a cell-vertex finite volume algorithm. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.