Ceramic monoliths first developed for their use in automotive catalyst, are used now to perform three-phase, catalyzed reactions. The large mass transfer rates achieved within this type of reactor are the result of large interfacial area and very thin diffusion paths. These enhanced mass transfer rates are credited to the presence of well-developed bubble-train flow. Bubble-train flows consist of trains of long bubbles separated by liquid slugs. The interfacial area is the area of the bubbles and the thin films are the result of the squeezing action of the bubbles as they overtake the liquid slugs. The objective of this paper is to predict the main mass transfer parameters, such as bubble size and shape, bubble velocity, and volume fraction of gas inside capillaries of circular or square cross section, on the basis of the superficial flow rates of gas and liquid in the feed. Experiments are reported here on bubble train flow inside capillaries of circular and square cross section for a large range of capillary numbers. A mass balance model was developed to allow the computation of flow parameters using an iteration scheme.