A shape retention hose construction and method of making the same are provided, the hose construction comprising a length of flexible tubular hose formed mainly of polymeric material and having opposite end portions and an intermediate body portion that defines internal and external peripheral surfaces of the hose, and a shape retention unit carried by the hose and being adapted to generally retain the shape of the hose construction when the hose and its carried shape retention structure are jointly bent into a particular shape, the shape retention unit comprising a deformable elongated member having opposed ends, the hose having a radially outwardly disposed and longitudinally extending projection on the external peripheral surface thereof, the elongated member being longitudinally disposed in the projection, the projection having opposed ends that respectively are disposed inboard of the opposite end portions of the hose, the opposed ends of the elongated member also being respectively disposed inboard of the opposite end portions of the hose, the end portions of the hose respectively having external peripheral surfaces that have substantially circular cross-sectional configurations through-out the axial lengths thereof.