Detailed prediction of groundborne noise and vibration from proposed rail transportation systems involves characterization of ground vibration propagation characteristics specific to sites with sensitive land uses along a project alignment. The methodology widely used in the United States relies on transfer mobility measurements performed at a limited set of locations, the results of which are typically used to characterize an entire corridor. Numerical and analytical models for predicting ground response can be used to interpret data, address limitations of field measurements, and refine predictions at locations where only soil strata data are available. FEA can be used to model the vibration response of the ground, as well as that of building foundations, tunnels, and other structures that often add complexity to the prediction problem. In this paper, we examine the ground surface response to an impulsive force via a transient response analysis performed using FEA to obtain one-third octave band transfer mobility functions. Analytical and numerical model results for a buried pulse in rock are presented and show general agreement with empirical data. Techniques used to address some of the limitations associated with modeling elastic wave propagation in semi-infinite media are discussed.