A model is presented to study the hypothesis that closure of pulmonary airways occurs as a result of an instability of the liquid layer lining the airway walls. Recent experimental results are reviewed that lead to predictions of closure, based on statically stable configurations, in the terminal bronchioles of the lung when lung volumes fall to about 20% of maximal lung volume. An approximate numerical model is developed to examine the dynamic process, simulating the collapse of the liquid film as airway volume falls during an expiration. Results are used to determine under what conditions the time-scale for film collapse is significant compared to typical expiration times.