The forced vibrations of railway vehicles are caused by excitations that appear during the rolling process, especially by the wheel-rail contact forces, which have a random distribution. Another example is represented by the internal forces that appear not only because of the force equipments inside the system or vehicle, which are not fully balanced for centrifugal forces, but also because of the gear boxes. The running stability of the rail-car is analyzed based on the proposed mechanical model and the general Lagrange equation. The amplitude amplification factor and the delay of oscillations are firstly analyzed theoretically, then graphically plotted in function of the non-dimensional normal pulsation for different values of the relative damping factor, both of the rail car suspension and the railroad. The possibility of improving the buffers for both coaches and trucks is analyzed in function of the non-dimensional normal pulsation for different transits of the rail cars through the resonance zone. The scope of the paper is to propose several different methods, both for goods and passengers wagons, regarding the damping aspects of the bouncing oscillations and suspension design. It leads to several important practical conclusions for the rail car designers and manufacturers.