A pressure-driven flow of elongated bullet-shaped bubbles in a narrow channel is known as Taylor flow or bubble-train flow. This process is of relevance in various applications of chemical engineering. In this paper, we describe a typical simplified experimental setting, with surface tension, density and viscosity as prescribed input parameters. We compare a sharp-interface model based on a moving grid aligned with the bubble boundary (ALE coordinates) and a diffuse-interface model where the bubble shape is implicitly given by a phase-field function. Four independent implementations based on the two modeling approaches are introduced and described briefly. Besides the simulation of the bubble shapes, we compare some resulting quantities such as pressure difference and film widths within the implementations and to existing analytical and experimental results. The simulations were conducted in 2D and 3D (rotationally symmetric). Good accordance of the results indicate the applicability and the usability of all approaches. Differences between the models and their implementations are visible but in no contradiction to theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.