Stress-induced demixing of a polymer solution is studied in the mainframe of the two-fluid theory. A true phase separation is predicted to take place and the theory has been reformulated so to be able to write the required boundary conditions at the interface between the two phases in terms of stress of the individual fluids. Also the free energy of mixing has been modified so to account for-the change of the entropy of mixing due to chain stretching. The predictions of the reformulated theory are compared with experimental data available in the literature showing a fair agreement. All the coupling effects between stress and concentration variations in a polymer solution can be now interpreted within a two-fluid theory framework so to have a universal picture of these phenomena. Indeed, the steady phenomena as the flow induced polymer migration and the enhancement of concentration fluctuations were already predicted in this mainframe, now, in this paper, also the true phase separation induced by steady flow is predicted with the two-fluid theory.