The flow of a bubble in non-Newtonian fluid can be observed in several industrial processes, from the production of food, chemical products or the drilling of an oil well. The study of this type of flow is done to optimize these processes in the best way possible. Drilling an oil well, for example, understanding the behavior of this multiphase mixture is extremely important to avoid the phenomenon called kick, which is an influx of unwanted fluids (water, gas, or oil) present in the formation into the well. This phenomenon can cause an uncontrolled flow of fluid on the surface, called blowout, which can lead to loss of control of the well causing accidents such as fires and other losses of all kinds. The study in general, seeks to determine bubble parameters, such as bubble velocity, bubble shape and diameter along the flow, among others. In this work, a numerical study of a single bubble flow in a non-Newtonian viscoplastic fluid is presented. This analysis is performed with the aid of FLUENT software, applying the VOF - volume of fluid method (Hirt and Nichols, 1981) [6] method to perform the calculations. The results obtained numerically will be compared with the results obtained experimentally by William F. Lopez in his work: Experiments of air bubble rising in yield stress fluids [1]. The results were obtained using a solution composed of the polymer Carbopol 980 NF dissolved in water, for different compositions of the polymer. Since the viscosity of a viscoplastic non-Newtonian fluid varies as a function of strain rate, we used the Herschel-Bulkley model for the determination of fluid viscosity in this study.