In the present work a constitutive model is developped in order to reproduce the rheological behaviour of waxy crude oils near and below their pour points, as wax starts to leave the liquid phase dependency of such behaviour on the previous thermak history of the oil and, later, the effects of shear rate are included by fitting it to a generalized Power Law model. The accuracy is verified on a test loop specially built to hand such oils and, although the predicted values are not in total agreement with measured ones, the qualitative behavior is well reproduced and further efforts should take place in order to get a test loop where the shearing effect, due mainly to the pump, will not interfere that much.