A theoretical investigation has been conducted for the prediction of the critical height at the onset of gas entrainment during single discharge from a stratified, two-phase region, through a branch installed on an inclined flat wall. The predicted critical height at the onset of gas entrainment was proven to be a function of Froude number (Fr) and density ratio of the interface fluids. Three different experimental data sets at wall inclination angles of zero, 45 and 90 degrees (i.e. side, inclined and bottom branches) were used for comparisons. A good concurrence was illustrated between the experimental and theoretical values.