Mesoscale Brownian dynamics simulations were performed to study the structures and theological properties of dilute solutions of flexible micelles. The micelles were modelled by chains of rigid rods. The scission energy and bending potential were introduced to model the interactions of micellar rods. The spatial distributions and orientations under shear flow were investigated. The transient stresses after the start-up of shear flow and steady-stare theological properties were also investigated. The simulation results showed that the transitions of the structure under shear flow and the theological properties vary with the scission energy and flexibility of the micelles. (C) 2013 Elsevier Ltd. All rights reserved.