This paper describes a 3D-model developed for the prediction of vibrations near a railway track. It consists of a track model lying on a layered ground and submitted to a moving train. It includes all elements of the track (rails, pads, sleepers and ballast) and allows a parametric analysis of its different elements and evaluation of vertical displacements according to the speed, the weight and the composition of the trains. Then in situ measurements are introduced with a view to the validation of the numerical model. A parameter study of the ground undertaken by seismic measurements shows a critical speed near 100 m/s while the studied trains are moving with sub-Rayleigh speeds (20 to 50 m/s). Consequently, all the parameters needed for the numerical model are defined. Many measurements were performed with a fast numerical camera which allows to notice the sheer size of the stress subjected to the track. Synchronised measurements of soil surface acceleration and track elements velocity were recorded. They give us a lot of informations about lateral and vertical displacements of track elements and at the soil surface. For highest speeds and freight trains, measured displacements reach more than about 10 millimetres. Finally, results are validated for different configurations. Measurements and simulation are compared in the time domain and in the term of spectral density. A comparison against distance of the track is also done and shows that contribution of the harmonic regime due to irregularities becomes more important farther from the track. The great agreement found in the validation confirmed the good quality of the determination of mechanical parameters, particularly the parameters which depend on compression and shear waves speed.