Work on flow limitation in elastic tubes of the body first relied on simple descriptions and intuitive modeling. Mathematical modeling led to the identification of a wave speed mechanism analogous to that of hydraulic flow in sluices and in supersonic nozzles. The basic pulse wave governs in the fluid-filled elastic tube. How this wave speed depends on the pressure-area characteristic of the tube is reviewed, and the determination of maximum flow rates for a given head, as in frictionless flow, is cited. The analysis of flow limitation for significant friction is briefly sketched, and the apparent paradox for viscous dominated flow still involving wave speed is resolved. Example applications include an analysis of density dependence of flow limitations, an exploration of implications concerning area and elastic modules at choke point for expiratory flow data is outlined, and predictions of flow from pressure-area characteristics are made. A summary of how airway system properties affect flow rates is given. Some of the difficulties of using flow data to infer airway properties are cited.