A flexible, stretchable, crush resistant hose particularly well suited for supplying breathing gases to patients in medical applications and the like has a helix defined by coils of thermoplastic material, and a web of thermoplastic material bonded or welded to adjacent ones of the coils, preferably along inner diameter portions of the surfaces of the coils. The web extends radially outwardly from between the adjacent coils to define a helical reverse-direction crease at a maximum outer diameter of the hose when the hose is in a normal minimal-length condition wherein the coils are situated side-by-side sandwiching portions of the web therebetween. The thermoplastic material of hose is stress relieved by an annealing process after the hose is formed, to enhance the flexibility of the hose and the ease with which the hose can be extended.