Two-phase bubble flow in a rectangular channel is simulated numerically by computing solutions to the Navier-Stokes equations for two-phase flow. The deforming boundary separating the gas and the liquid is modeled numerically using the coupled level-set/volume-of-fluid (CLSVOF) method. In this study, we confine ourselves to two-dimensional computations in a rectangular domain. Even two-dimensional computations allow the prediction of two-phase bubble flows in a rectangular channel. It is shown that our computational results corroborate the previous study, in which it is reported that the liquid superficial velocity is lower in the region of transition to dispersed flow in a rectangular channel than in a similar transition channel in a circular pipe.