Stress induced demixing of a polymer solution is predicted by a two fluid theory reformulated to. be able to impose all the interface boundary conditions required. The theory has now been applied to the data on solutions of polystyrene in dioctylphthalate of Rangel-Nafaile et al. [Macromolecules 17, 1187-1195 (1984)] at one molecular weight at various temperatures, to additional unpublished data at various molecular weights, and to various published experiments in which there was evidence for phase separation. The dependence of elastic compliance on concentration was approximated by an equation which permitted the analytic differentiations and integrations required for the equations of the theory. The prediction of visual cloud point stresses at various temperatures were excellent within the concentration range over which the compliances had been fitted. The calculated demixing stresses were somewhat higher than those measured by extrapolation of photometric data to onset of turbidity, possibly because the onset correlates more closely to the occurrence of concentration fluctuations preceding demixing. The earlier kinetic theories that predict fluctuations but not demixing assumed a monotonic dependence of elasticity on concentration, contrary to theoretical and experimental results, and do not account for the light scattering observation of phase separation in shear flow. (C) 2003 The Society of Rheology.