Spectral element methods are developed for simulating viscoelastic flows based on a micro-macro modelling approach in which the polymer dynamics is described by the evolution of an ensemble of Brownian configuration fields. The application of the technique to the start-up of Couette flow and flow between eccentrically rotating cylinders are described. Comparisons are made between simulations based on the Oldroyd B constitutive model and those based on Brownian configuration fields using Hookean dumbbells. Comparisons are also made between simulations based on different force laws. The performance of the method is discussed. (c) 2006 Elsevier B.V. All rights reserved.