Modelling fibers orientation induced by the flow of short fibers reinforced thermoplastic suspensions is of major interest in composites processing. This mathematical modelling involves a classical anisotropic Stokes flow problem and a hyperbolic orientation equation on which this paper is specifically focussed. This paper addresses a theoretical result that concerns the uniqueness of a solution of this orientation equation in recirculating flows in steady state conditions. This result makes it possible to use the method of characteristics for recirculating flows. Results of these computations are then compared with other methods to evidence the strong limitation of SUPG or discontinuous finite volume techniques when they are applied to the flow of fibers suspensions. (C) 2000 Elsevier Science B.V. All rights reserved.