Summary: We perform a comparison of structurally-continual and phenomenological approaches to modelling the flow of viscoelastic fluid in a plane channel. A dilute suspension of rigid ellipsoidal particles in a Newtonian fluid is considered as viscoelastic fluid. The rheological behaviour of this suspension is investigated with the help of the second-order Rivlin-Ericksen fluid model. As a result of the above comparison, a considerable disagreement in pressure distribution (up to 40%) is observed. It raises a doubt that the Rivlin-Ericksen model (as any other complex phenomenological model) can be used for exact calculations of those flows in plane channel. A Delphi computer program was developed to carry out the computations.