In this work, a model for calculating the dynamic viscosity of polymer solutions was developed. The model is based on the Eyring absolute rate theory and on the solution theory of McMillan-Mayer. An equation of state is used for the calculation of the solution osmotic pressure and, thus, the excess molar McMillan-Mayer free energy. The final expression shows an explicit dependence between the viscosity of the polymer solution and the applied shear stress. The proposed model contains three terms. The first term describes the viscosity of an ideal polymer solution. The second term takes into account non-Newtonian behavior of the polymer solution. Finally, the third term represents the deviation from the thermodynamic ideal behavior. The whole model presented five adjustable parameters, with two of them also considered as being a function of the applied shear stress. To test the proposed model, we have measured experimental rheological data for poly(ethylene glycol) aqueous solutions (nominal molecular weight 6000 g/mol) for nine different polymer concentrations, at different shear rates, at 313.15 K and 0.1 MPa. The proposed model has been used for correlating the experimental viscosity data of these polymer solutions at different values of the applied shear stress and polymer concentration. It has been found that the agreement between the experimental and calculated values is within the experimental error.