The model of the low capillary number propagation of a liquid plug or bolus through an elastic tube has been presented using lubrication theory and matched asymptotic expansions. The authors investigate criteria for airway opening, and analyze the dependence of these on physiological parameters such as surface tension, airway lining thickness and airway wall elastic properties. In the limit of small capillary number, asymptotic expressions are obtained for the pressure drop across bolus and for the thickness of the liquid film left behind, as functions of the capillary number, the thickness of the liquid lining ahead of the bolus, and the elastic characteristics of the tube wall. The dimensionless wall compliance is assumed to be sufficiently small, so that the wall displacements are of the same order as the thickness of the liquid lining. The authors calculate the critical pressure drop that must be imposed across the bolus if the thickness of the film it leaves behind is to exceed that of the film ahead of it. This gives a minimum criterion for eventual rupture of the bolus and for reopening of the tube. Finally, the authors develop a theory for bolus propagation through a relatively compliant tube in the tension-dominated case, and identify the minimum criterion for tube reopening.