An instability resembling an avalanche is proposed as the mechanism by which mucus is expelled from the respiratory tract during cough. The cough event was simulated in a model airway. In these experiments, air was forced through a channel whose walls were lined with a non-Newtonian material rheologically similar to tracheal mucus. Frames from high-speed cine photographs showed an unstable event which began as an undulation of the free surface and progressed to a catastrophic clearance of the channel. Measurements of the longitudinal pressure gradient support the hypothesis that the clearance event is initiated when the total stress applied to the mucus analog exceeds its finite yield stress. A continuum model predicts that yielding occurs within the bottom layers of the mucus analog. Calculations based upon estimates of tracheal geometry and air flow show that the clearance event studied here would be expected to occur during a cough but not during normal breathing. Experiments also show that a lubricant introduced between the channel walls and the mucus blanket can reduce the air flow rate required to precipitate the clearance.