A numerical method to simulate fibre suspensions in transient and steady state shear flows for concentrated solutions is reported, which takes into account short-range hydrodynamic interaction via lubrication forces, contact forces and hydrodynamic forces. Fibres are assumed to have varying lengths as observed in industrial composites and this can be described with a fibre distribution length function. Stresses in the composite have been calculated from a constitutive equation or from an approximate expression for the effective stress of fibre suspensions. This simulation will assist in modelling of short fibre filled industrial composites. Our first results shown here qualitatively agree with experiments. (c) 2006 Elsevier B.V. All rights reserved.