When trains run on soft ground, large deflections of the track and vibration of the ground can occur when the train speed approaches the speed of Rayleigh waves in the ground. Modelling is helpful to understand and mitigate such critical velocity effects. Here, a three-dimensional time-domain model of a load moving on a track and ground has been developed with the finite element software ABAQUS. This allows nonlinear soil properties to be considered. In order to validate the approach, the vibration of the track and ground induced by a high speed train is compared with those from the site measurements carried out in the late 1990s at Ledsgård, Sweden. Due to the particularly soft soil at this site, it is necessary to adopt a nonlinear soil model due to the large deflections induced by the high-speed train. It is shown that using a linear model based on the small strain soil parameters leads to results which underestimate the displacements. Laboratory test data allow the nonlinear characteristics to be obtained. These have previously been used by various authors in an equivalent linear model. Here this approach is compared with a fully nonlinear model.