In the horizontal drilling process, due to the weight of the drill string, the column may be located at a lower portion of the wellbore, thereby exhibiting an eccentric configuration. It is important to predict the eccentricity effect on the drilling fluids flowing through the annular, a subject not often discussed in the literature. The fluid dynamics of non-Newtonian fluids (xanthan gum solutions) flowing through annuli with the variable eccentricity motion of the inner tube was investigated. The effects of four important operating variables were quantified. The comparison between computational fluid dynamics simulations and the experimental data indicated a very good agreement.