Cementing job is a crucial operation in the construction (drilling operation) of an oil and gas well. The cement must be placed in annulus geometry between the steel casing and the wall of the well. The key to a successful cement job is the complete removal of mud from the annulus by cement slurry that is pumped down through the casing and return up by the annulus space. The correct prediction of the flow and consequently of the displacement of the fluids is very important, because poor displacement require remedial squeeze cementing which is both costly and time consuming. A complete analysis of this situation is extremely complex: the steel casing is eccentric and the eccentricity varies along the well, the wellbore wall will depart significantly from cylindrical, the inclination of the well affects the flow, fluids are non-Newtonian and flow is extremely dependent of the rheologies of the fluids. A complete analysis of this situation would require the solution of the three-dimensional momentum equation and would be computationally expensive and complex. Models available in the literature to study this situation do consider the non-Newtonian behavior of the drilling fluids, but assume the relative position of the inner with respect to the outer cylinders fixed, neglecting the variation of the eccentricity along the well and the flow is considered to be fully developed. This approximation leads to a two-dimensional model to solve the velocity field of the flow. The model presented in this work takes into account the variation of the eccentricity along the well and the inclination of the well, a more appropriate description of the configuration of directional wells. Lubrication theory is used to simplify the three-dimensional governing equations into a two-dimensional differential equation that describes the pressure field. The differential equation was solved by the finite difference method (central difference). Once the pressure field is known, the velocity field can be found and the displacement of the mud (drilling fluid) in annulus can be evaluated explicit as a time function.