The finite length nature of rail-pad supports is characterised by a Timoshenko beam element formulation over an elastic foundation, giving rise to the distributed support element. The new element is integrated into a vertical track model, which is solved in frequency and time domain. The developed formulation is obtained by solving the governing equations of a Timoshenko beam for this particular case. The interaction between sleeper and rail via the elastic connection is considered in an analytical, compact and efficient way. The modelling technique results in realistic amplitudes of the pinned-pinned' vibration mode and, additionally, it leads to a smooth evolution of the contact force temporal response and to reduced amplitudes of the rail vertical oscillation, as compared to the results from concentrated support models. Simulations are performed for both parametric and sinusoidal roughness excitation. The model of support proposed here is compared with a previous finite length model developed by other authors, coming to the conclusion that the proposed model gives accurate results at a reduced computational cost.