An analytical model was developed to predict the critical conditions at 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 upstream inlet region. The branch flow was simulated as a three-dimensional point-sink while the downstream run flow was treated with a uniform velocity at the critical dip location. A boundary condition was imposed in the model whereby the flow distribution between the branch and run was obtained experimentally and digital imaging was used to quantify the critical dip location through the dip angle. Three constant dip angles were evaluated in the model and results showed the dip height to have good agreement with experiments between angles of 50 and 60 degrees. The predicted upstream height, however, did not match well with the experimentally determined height due to the omission of shear and inertial effects between the upstream location and critical dip.