A new criterion has been developed to predict the onset of liquid (heavier fluid) entrainment from a stratified two-phase region. The criterion was developed based on the local instability of the interface between two fluids due to the suction effect associated with the discharging of the lighter fluid. To validate the proposed criterion, comparisons were conducted between the measured critical height at the onset and those predicted using a three-dimensional analysis of the flow through two configurations: (1) a single branch mounted on an inclined wall with an inclination angle ranging between −90° and + 60° and (2) dual branches mounted on a vertical wall with the plane passing through the branch centerlines and inclined with an angle α ranging between 0° and 60°. Comparisons demonstrate a very good agreement between the predicted and the measured values for both single and dual branches. This verifies that the onset of liquid entrainment mechanism occurs due to local flow instability of the interface, analogous to Rayleigh–Taylor instability.