This hybrid finite element/volume study is concerned with the modelling of worm-like micellar systems, employing a new micellar thixotropic constitutive model with viscoelasticity within network-structure construction-destruction kinetics. The work focuses on steady-state solutions for axisymmetric, rounded-corner, 4:1:4 contraction-expansion flows. This has importance in industrial and healthcare applications such as in enhanced oil-reservoir recovery. Material functions for the micellar models (time-dependent, thixotropic) have been fitted to match two different extensional configurations of the exponential Phan-Thien/Tanner (PTT) model (rubber network-based, non-thixotropic). This covers mild and strong-hardening response, and re solvent fraction, highly-polymeric (beta = 1/9) and solvent-dominated (beta=0.9) fluids. Solution results are described through normalised Excess Pressure Drop (EPD), vortex intensity and stream function, stress (N-1 and N-2), and f-functional data. EPD predictions with the new micellar models prove to be consistent (at low rates, some rising) with Newtonian results, contrary to the base-reference modified Bautista-Manero (MBM) results. Markedly different vortex intensity trends are found in comparing micellar and EPTT solutions, which correspond with N-2 - N-1 and f data. In order to address the highly-elastic regime for thixotropic materials, a convoluted approach between EPPT and micellar models has been proposed. Here, numerically stable solutions are reported for impressively large We up to 300 and new vortex structures are revealed. (C) 2013 Elsevier B.V. All rights reserved.