This system for fastening a rail comprises an elastically yieldable fastener and a clamping device which extends through the fastener, an elastically yieldable block provided with a central aperture for the passage of the clamping device and a cap. The cap is in the form of a cup which is provided with a central aperture and is extended around the cup aperture by a tubular sleeve. The block is placed in the cap. The internal volume of the cap is less than the volume occupied by the block when it is compressed, whereby, in the course of the clamping of the clamping device, the lateral expansion of the block is limited by the cap and its axial elasticity is maintained.