Hydraulic shock-absorber for a vehicle suspension, comprising a first cylindrical tube , a rod which is arranged coaxially with the first cylindrical tube and projects partially therefrom, and a piston attached to an end portion of the rod , the piston being slidably mounted in the first cylindrical tube and separating the inner volume of the first cylindrical tube into a rebound chamber and a compression chamber in which a damping fluid is contained, the shock-absorber further comprising a first valve assembly on the piston , a second valve assembly on the bottom of the compression chamber , and a hydraulic stop member which is mounted in the compression chamber and is adapted to operate during the compression stroke of the shock-absorber to hydraulically dissipate kinetic energy when the piston of the shock-absorber moves towards a compression end-of-travel position, wherein the hydraulic stop member comprises a cup-shaped body , which is mounted in a bottom area of the compression chamber of the shock-absorber , coaxially therewith, and a plunger , which is mounted on the rod of the shock-absorber , coaxially therewith, on the same side as the piston of the shock-absorber , so as to slide in the cup-shaped body when the piston of the shock-absorber is close to the compression end-of-travel position, wherein the cup-shaped body comprises a side wall and a bottom wall which define, along with the plunger of the stop member , a working chamber in which the damping fluid is compressed by the plunger of the stop member when the latter slides in the working chamber towards the bottom wall of the cup-shaped body during the compression stroke of the shock-absorber , wherein axial channels are formed on the inner surface of the side wall of the cup-shaped body , which axial channels extend parallel to a longitudinal axis (z) of the cup-shaped body and are configured to allow the damping fluid to flow axially out of the working chamber when the plunger of the stop member slides in the working chamber towards the bottom wall of the cup-shaped body , said axial channels having a cross-section whose area decreases continuously along the longitudinal axis (z) towards the bottom wall of the cup-shaped body , and wherein the side wall of the cup-shaped body comprises a first wall portion of cylindrical shape, which faces towards the opposite side of the bottom wall of the cup-shaped body and is securely connected to the first cylindrical tube inside the compression chamber , a second wall portion of cylindrical shape, which faces towards the bottom wall of the cup-shaped body and has an outer diameter smaller than the inner diameter of the first cylindrical tube , and a third, tapered wall portion , which connects the first wall portion with the second wall portion , said axial channels being formed on the inner surface of the second wall portion , characterized in that the first wall portion has an outer diameter substantially equal to the inner diameter of the first cylindrical tube , in that an annular passage is defined between the second wall portion and the first cylindrical tube and is in fluid communication with the portion of the compression chamber underneath the bottom wall of the cup-shaped body , and in that the side wall of the cup-shaped body has first passages configured to put the portion of the compression chamber comprised between the piston of the shock-absorber and the plunger of the stop member into communication with the second valve assembly in the bottom area of the compression chamber of the shock-absorber . <EOS>