Precipitated wax, shear and thermal history have pronounced effects on viscosity and rheological behavior of waxy crudes. On the basis of mechanism of waxy crude rheology, a shear-rate-dependent viscosity model has been developed by applying theory of suspension rheology. This model is characterized by its capability to predict viscosities of crude oils with various thermal and shear history and beneficiated with pour-point-depressants (PPD). Once viscosities at only two temperatures above the wax appearance temperature and apparent viscosities at one temperature in the non-Newtonian regime are known, viscosities or apparent viscosities at any temperatures above the gel point can be predicted by using the model together with the concentration of precipitated wax at that specified temperature. Verification by using 3458 viscosity data points ranging from 5 to 2900 mPa s from 33 virgin crudes and 14 PPD-beneficiated crudes with various thermal and shear history shows that the model predicts viscosities with an absolute average deviation of 7.43%. Furthermore parameters of rheological models such as the consistency coefficient K and the flow behavior index n of the power law model may be obtained by regressing predicted viscosity data and corresponding shear-rates. (C) 2003 Elsevier Science Ltd. All rights reserved.