A new theoretical non-Newtonian viscosity model is developed by taking the fractional series expansion of Eyring's shearing strain rate. A broad range of experimental rheological data of various polymer melts including polyethylenes, polypropylene, polystyrene, poly (methyl methacrylate), and polycarbonate are fitted well using the proposed model. From the model; zero shear, constant shear-stress and constant shear-rate viscosities are derived as a linear function of viscosity related quantity, Y-h, called thermo-occupancy function and their coefficients are discussed in detail. The thermo-occupancy function is expressed in terms of temperature and structural vacancies such as hole fraction computed from the Simha-Somcynsky Hole Theory (SS). In addition, the derivative of the logarithm of viscosities with respect to the hole fraction, named as viscoholibility, is observed decreases with the increasing hole fraction. (c) 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40540.