Rheological behavior is key for the evaluation, simulation, and development of petroleum reservoirs. In previous papers, friction theory models have been used to develop accurate, even reference quality, descriptions of the Newtonian shear viscosity of fluids. The friction theory has also been successfully used to accurately model an ample range of reservoir fluids ranging from natural gas to heavy oils (with viscosities up to thousands of mPa s). In this work, the basic friction theory approach has been further extended to the description of the non-Newtonian shear viscosity of crude oils. The extension is carried out by modifying the basic approach by further introducing a shear rate dissipation parameter for the scaling of the non-Newtonian behavior and a wax-appearance-related temperature. The resulting approach is straightforward and can reproduce the non-Newtonian behavior of crude oils with an accuracy close to the experimental uncertainty. The extended model is consistent with the overall friction theory approach and can be applied to the full range of oil reservoir production conditions, which is demonstrated by the ability of the model to calculate the expected theological properties of a reconstituted reservoir fluid. In its current form, the proposed model has three adjustable parameters for a full characterization of the investigated oils, and no further parameters are needed in case the fluid is reconstituted. The model is able to reproduce the experimental Newtonian and non-Newtonian theology over the wide temperature ranges of the studied waxy oils to within an overall average absolute percentage deviation under 15%. Consistent with previous investigations, the addition of a natural gas should yield lower deviations for the reconstituted fluid.