The interrupter method for measuring respiratory system resistance involves rapidly interrupting flow at the airway opening while measuring the pressure just distal to the site of interruption. In general, the pressure signal obtained exhibits an initial rapid change (delta Pinit) accompanied by rapid damped oscillations, followed by a further slow change to a steady-state plateau level. Delta Pinit is thought to principally reflect the resistance of the pulmonary airways Raw. We have developed a computer model capable of simulating the main features observed in an interrupter pressure signal. We show that the distinct phases in the pressure signal can be obscured by the existence of a compliant compartment between the airways and the occluding valve (e.g. the cheeks and pharynx) when Raw is increased. Our results suggest that supporting the cheeks may enable one to estimate Raw with the interrupter technique in the presence of mild to moderate bronchoconstriction, but that with severe bronchoconstriction (Raw increased 10-fold above normal) it may not be possible.