In the present study, the displacement of waxy crude oils is numerically/theoretically investigated in the water-flooding operation. The oil was assumed to obey the Houska model-a robust thixotropic fluid model which is often realized to well describe the rheology of waxy oils in different parts of the world. Based on the concept of effective viscosity, a modified version of the Darcy's law was developed for this particular fluid model in order to describe its flow through a homogenous porous medium. Use was made of numerical and theoretical methods to study the displacement of Houska fluid by water in two benchmark problems: (i) the Buckley-Leverett problem, and (ii) the five-spot problem. It was found that the yield stress of the Houska fluid being variable (i.e., shear- and time-dependent) has a retarding effect on the water breakthrough phenomenon. The breakdown-to-rebuild ratio in the Houska model was shown to play a key role in the water breakthrough phenomenon provided that it is very large. At this extreme, however, the effect was attributed mostly to the shear-thinning behavior of the Houska fluid rather than its thixotropic behavior. In fact, at sufficiently low breakdown-to-rebuild ratios (i.e., when fluid's thixotropy becomes progressively more important) it had no significant effect on the water breakthrough phenomenon. Therefore, it is concluded that in competition with shear-thinning, the thixotropic behavior of Houska fluid plays a secondary role, if any, in the water-flooding operation. (C) 2016 Elsevier B.V. All rights reserved.