A number of different models are used to describe the shear rate dependent viscosity of drilling fluids. Most, such as the Herschel-Bulkley model, have a purely empirical basis. The Quemada model, while still empirical, is based on physical principles. It is based on the notion that structural units develop in the fluid at low shear rates which are then partially broken down as the applied shear rate increases. In the current work, drilling fluid rheological data are fitted to the Herschel-Bulkley and the Quemada model. The development of the Quemada model and the calculation of each model parameter are presented. We show that the Quemada model better fits measurements over a wider range of shear rates than the Herschel-Bulkley model. We describe how to select the parameters of the Quemada model. Knowing the difficulty of obtaining a known shear rate for fluids with yield stresses, we discuss how this can affect the quality of the Quemada model fit. Furthermore, in principle, the Quemada model is not applicable in presence a non-zero yield stress. Therefore, we show how to handle the yield stress using a (very high) zero shear rate viscosity.