A flexible, stretchable, crush resistant hose particularly well suited for supplying breathing gases to patients in medical applications and the like is formed by providing a helix of coils of thermoplastic material that are bonded to a web of thermoplastic material, preferably along inner diameter surface portions of the coils. The web extends radially outwardly from between 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 performed while the hose is axially compressed after the hose is formed.