A helically convoluted hose clamp has a central portion of rectangular cross-sectional outline, two intermediate portions of rectangular or V-shaped cross-sectional outline, and two radially outwardly extending end portions. The moments of resistance of the intermediate portions exceed the moment of resistance of the median portion, and the overall length of the clamp is in excess of 1.5 convolutions preferably between 2.5 and 2.6 convolutions. The inner diameter of the clamp is normally less than the outer diameter of the hose which is to be clamped on a pipe or the like. The length of the intermediate portions exceeds the length of the end portions, and each such intermediate portion can extend along an arc of approximately 360 degrees. Pronounced moments of resistance of the intermediate portions promote the clamping action and prevent the end portions from yielding and bending when they are acted upon to increase the inner diameter of the clamp.