An analytical study on the limit conditions of steady-state countercurrent annular flow in a vertical tube has been performed, aiming at the prediction of the onset of flooding in tubes where it is difficult for unstable wave motion to occur. A new expedient method is developed to determine the limit conditions under the involved flow conditions. It is revealed that the limit conditions in this flow system appear only when the interfacial shear stress increases with the liquid film thickness. A prediction model that takes the full effects of the void fraction epsilon into account, and a simplified model that considers only the effect of the liquid film thickness on the interfacial shear stress under a fixed condition of epsilon = 1 are dealt with, showing that they predict the experimental data fairly well at low liquid flow rates, and that the latter model performs better than the former one. Finally, there is a brief discussion as to the possibility of the application of the present analysis to the prediction of the critical heat flux of boiling in a bottom-closed vertical tube.