The elastically yieldable fastener comprises an elastically yieldable strip bent onto itself and forming two superimposed branches. A clamping device extends through apertures in the two branches for clamping the strip to the support of the rail. The upper branch has a boss disposed between the aperture of the upper branch and the free end of the latter and between lateral portions of the upper branch which are adapted to bear against the lower branch when the strip is clamped by the clamping device. The clamping device defines a lower surface for contacting the upper surface of the boss and the two surfaces have the same shape so that, in the normally clamped position of the strip, the portion of the branch carrying the surface contacting the clamping device is raised with respect to the lateral portions.