A rotor for turbomachines having a plurality of blades, and a damping member housed inside a chamber respectively arranged between each pair of adjacent blades of the rotor. The damping member is pushed, in use, by the centrifugal force against two surfaces, each of which is carried by a respective blade, which limit the respective chamber in a radially outward direction. The damping member is cup-shaped and provided with a base wall facing the two surfaces of the chamber and has three support bosses provided on one surface so that at least one of the three will contact one of the two surfaces and at least one other will contact the other of the two surfaces.