A thermodynamic approach for modeling the phase equilibrium of multicomponent fluid mixtures under the influence of an applied shear rate (shear stress) is presented. This approach is based on assuming that, for the modeled mixtures, the viscosity variation with shear rate can be well-described by using a power law. This framework is then used for predicting the influence of shear rate on the critical temperature, critical pressure, and spinodal curve of several Newtonian multicomponent hydrocarbon mixtures; giving as a result that for these kind of mixtures and depending on the composition, the critical temperature exhibits both an upward and downward shift with shear rate, whereas the critical pressure always exhibits a downward trend. Both a suppression of the liquid-liquid transition and shrinkage of the spinodal curves (mixing effect) are also predicted. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 4383-4389, 2013