A model was developed to predict the onset of gas entrainment in a single downward oriented branch. The branch was installed on a horizontal square cross-sectional channel having a smooth stratified co-currently flowing gas-liquid regime in the inlet region. The branch flow was simulated as a three-dimensional point-sink while the run flow was treated as a uniform velocity at the critical dip. Experiments were performed to determine the critical liquid flow distribution between the run and the branch. A correlation was developed relating the branch Froude number to the ratio of the superficial liquid mass fluxes in the run and the branch. The correlation was used as a boundary condition in the model. A methodology was developed using digital imaging to record the coordinates of the critical dip at the onset of as entrainment. The dip angle was found to range between 40 to 60 degrees and constant dip angles of 40, 50 and 60 degrees were selected as boundary conditions. The critical height was predicted to within 50% of experiments with the error attributed to differences in the modeled and experimental geometries. A semi-empirical analysis using the experimental geometry yielded a critical height prediction to within 20% of experimental results.