There is an increasing interest in applying three-dimensional computational fluid dynamics (CFD) for multiphase flow transport in pipelines, e.g., in the oil and gas industry. In this study, the volume of fluid (VOF) multiphase model in a commercial CFD code was used to benchmark the capabilities. Two basic flow structures, namely, the Benjamin bubble and the Taylor bubble, are considered. These two structures are closely related to the slug flow regime, which is a common flow pattern encountered in multiphase transport pipelines. After nondimensionalization, the scaled bubble velocity (Froude number) is only dependent on the Reynolds number and on the Eötvös number, which represent the effect of viscosity and surface tension, respectively. Simulations were made for a range of Reynolds numbers and Eötvös numbers (including the limits of vanishing viscosity and surface tension), and the results were compared with the existing experiments and analytical expressions. Overall, there is very good agreement. An exception is the simulation for the 2D Benjamin bubble at a low Eötvös number (i.e., large surface tension effect) which deviates from the experiments, even at a refined numerical grid.