There are many industrial machines that function by operation of multi-phase fluids. Some of them take advantage of the characteristics of counter-current two-phase flow. The maximum flow rates of gas and liquid phases which flow in opposite-directions (counter-current flow) are limited by a phenomenon known as a Counter-Current Flow Limitation (CCFL or flooding). The mass and momentum conservation equations for two phases were established to build a system of first-order partial derivative equations (PDE). A new CCFL model was developed based on the characteristic equation of the first-order PDE system. The present model applies to the case in which a non-uniform flow is developed around a square or sharp-edged entrance of liquid phase. The model can be used to predict the operating-limit of components in which mass and heat transfer are taking place between liquid and gas phases.