We explore the theological predictions of a constitutive model developed for dilute or semi-dilute worm-like micellar solutions in an axisymmetric Taylor-Couette flow. This study is a natural continuation of earlier work on rectilinear shear flows. The model. based on a bead-spring microstructure with non-affine motion, reproduces the pronounced plateau in the stress-strain-rate flow curve that is observed in laboratory measurements of steady shearing flows. We also carry out a linear stability analysis of the computed steady-state solutions. The results show shear-banding in the form of sharp changes in velocity gradients, spatial variations in number density, and in alignment or stretching of the micelles. The velocity profiles obtained in numerical solutions show good qualitative agreement with those of laboratory experiments. (c) 2006 Elsevier B.V. All rights reserved.