A theoretical investigation has been conducted for predicting the critical liquid height at the onset of liquid entrainment during dual discharge from a stratified two-phase region through branches mounted on an inclined flat wall. The centerlines of the two branches are parallel and they fall in a common vertical plane. Two models have been developed; a simplified point-sink model and a more-accurate finite-branch model. Predictions from the two models are shown to be in good agreement for the condition of high flow rates from the branches, while the finite-branch model is necessary for accurate predictions at low branch flow rates. This behaviour has been confirmed experimentally for the vertical-wall configuration.