A fuel pump for a direct injection system having: at least one pumping chamber; a piston which is mounted sliding inside the pumping chamber in order to vary cyclically the volume of the pumping chamber; an intake duct connected to the pumping chamber and regulated by an inlet valve; a delivery duct connected to the pumping chamber and regulated by a one-way delivery valve which allows exclusively a fuel flow outgoing from the pumping chamber; and a damping device, which is placed along the intake duct upstream of the inlet valve, and comprises at least one elastically deformable damping body that has internally a closed chamber filled with pressurized gas and composed of two metal plates cup shaped and welded together at their annular edges by an annular weld without interruptions.