A check-valve model has, been described for the purpose of understanding the characteristics of the expiratory flow. The diameter changes of the bronchi and the pressure distribution in the flow direction are calculated by a digital simulation technique. It is assumed that the airway is composed of the bifurcate branches which are the collapsible tubes with finite length because the ratio of the diameter to the length of the bronchi is not so small, the rigidity of bifurcations should not be ignored, and the displacement of the diameter caused by airflow is not so large. Mathematical expressions are derived and some calculated results are obtained in the case of circular cross section. In these numerical computations, the values given by Weibel's model is used as the geometry of the bronchial tree, and the effects of the expansion losses and the lung parenchyma are taken into account in a simple manner. It is found that the saturation of flow in IVPF (iso-volume-pressure-flow) curve is significantly affected by the compression of the branches between 2nd and 4th, and that maximum flow has dependence on the properties of bronchial wall, flow density and the degree of lung inflation related with the lung parenchyma. These results approximately coincide with the experimental results qualitatively and quantitatively in the overall IVPF characteristics under reasonable values of some parameters.