Abstract: An extruded bead of thermoplastics material and an extruded tape-like web of thermoplastics material are wrapped in a coordinated manner around a rotating mandrel to continuously form a corrugated, helically reinforced, uniquely constructed “stretch hose” having a thread-like exterior appearance dominated by the web extending in an inclined spiral as it bridges from an outer diameter of each reinforcing coil to an inner diameter of the next-formed reinforcing coil. When the hose is axially compressed, the thin web-defined wall that connects each adjacent pair of reinforcing coils advantageously has one portion that bends or folds radially outwardly, and another portion that bends or folds radially inwardly. Discrete lengths of the hose are treated to minimize stress, to reset memory, and to greatly enhance hose flexibility.