Heavy freight trains emit ground vibration with predominant frequency components in the range 4-30 Hz. If the amplitude is sufficient, this may be felt by lineside residents, giving rise to disturbance and concern over possible damage to their property. In order to establish the influence of parameters of the track and rolling stock and thereby enable the design of a low vibration railway, a theoretical model of both the generation and propagation of vibration is required. The vibration is generated as a combination of the effects of dynamic forces, due to the unevenness of the track, and the effects of the track deformation under successive axle loads. A prediction scheme, which combines these effects, has been produced. A vehicle model is used to predict the dynamic forces at the wheels. This includes the non-linear effects of friction damped suspensions. The loaded track profile is measured by using a track recording coach. The dynamic loading and the effects of the moving axles are combined in a track response model. The predicted track vibration is compared to measurements. The transfer functions from the track to a point in the ground can be calculated by using a coupled track and a three-dimensional layered ground model. The propagation effects of the ground layers are important but the computation of the transfer function from each sleeper, which would be required for a phase coherent summation of the vibration in the ground, would be prohibitive. A compromise summation is used and results are compared with measurements. (C) 1996 Academic Press Limited