EXACT SOLUTION OF THE PROBLEM OF FLOW OF A POLYMER SOLUTION IN A PLANE CHANNELS. N. Aristov and O. I. Skul'skii UDC 532.135 One-dimensional flow of polymer solutions in a plane channel under the action of the pressure gradient has been considered. To describe the rheological properties of the solutions we have selected: 1) generalization of the Jeffreys phenomenological model with an objective time derivative Fabc with six arbitrary material constants; 2) the differential vector model proposed by Remmelgas, Harrison, and Leal and that is the approximation of the Doi-Edwards-Marrucci-Grizzuti model. Exact analytical solutions of the problem of flow in a plane channel have been obtained for them. In the two cases the problem can have both a unique solution and a nonunique solution. The velocity profiles are either smooth nearly parabolic or have weak tangential discontinuities. Criterial conditions for the appearance of ambiguous flow regimes have been obtained. Institute of Continuum Mechanics, Ural Branch of the Russian Academy of Sciences, Perm', Russia; email: firstname.lastname@example.org. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 3, pp. 88-95, May-June, 2003. Original article submitted September 6, 2002.