The paper focuses on the influence of the longitudinal and lateral suspension damping in correlation with the velocity upon the vibration behaviour of the railway vehicles while moving on a tangent track. The numerical simulations are developed based on a linear model of a 17-degree of freedom vehicle that allows the evaluation of the dynamic behaviour of the vehicle in a sub-critical velocity. Based on the response frequency functions of the vehicle in a harmonic and in a random behaviour, a series of basic properties of the stable behaviour of the forced lateral vibrations has been made evident, as well as the opportunities to lower the level of the carbody vibrations by changing the suspension damping.