The study of flows in the annulus is essential for the understanding of the cementing process of oil wells. The drilling mud must have rheological properties to guarantee a good performance in the drill lubricating/ cooling, dragging cuttings until the surface, as well as keeping the well pressure due the hydrostatic column. During the cementing, this mud must be removed and substituted by cement slurry. The cement has the function to coat the wall of the formation, promoting the mechanical stability and preventing infiltrations. The process of substitution occurs by the displacement of a fluid by another one in the annulus between the rock formation and the casing. To improve the cementing process, intermediate fluids (washing or spacers) are used between the drilling mud and the cement slurry. Therefore, it is important to know the effect of the rheology of such fluids on the displacement process. Drilling mud and cement slurry have a viscoplastic behavior. Such materials have yield stress, below which the viscosity is extremely high. However, after this limit, these materials have pseudoplastic behavior, that is, viscosity decreases as a function of the deformation rate. The washing fluid presents newtonian behavior. The rheological model SMD (Souza Mendes and Dutra) was used to describe the viscosity of the non-newtonian fluids. In this work, the process of displacement of a fluid for another one in non-straight horizontal wellbore was numerically analyzed. The drilling of horizontal wells uses a rotary steering technique aiming the drill positioning, adjusting the steering vector. However, a sine profile drilling is gotten, due to the technique of vertical compensation of the direction. Analyzed geometry will be developed in zigzag, to represent this behavior. It was used a commercial software to simulate the tree-dimensional displacement process, using the finite-volume technique, and the VOF (Volume of Fluid) method. Two steps of the process had been studied. In the first situation, the displacer fluid (non-newtonian) simulates the cement slurry while the displaced (newtonian) simulates the spacer fluid. In the second situation, the displacer fluid (newtonian) simulates the spacer fluid while the displaced (non-newtonian) simulates the drilling mud. The interface shape between the fluids has being evaluated varying the rheological properties and the flow, to determine the displacement efficiency. Accented profiles suggest an undesirable fingering of the displacer fluid through the displaced one. On the other hand, flattened profiles indicate a more efficient displacement. Based on these results, it was possible to predict which operational parameters optimize the displacement process.