Ballasted railway tracks are one of the most common structures travelled by high-speed trains. The high circulation speeds of these trains lead to increased vibrations in the tracks and nearby structures, which can affect the serviceability and maintenance costs of the tracks. There is a growing demand for a means of accurately predicting the performance of ballasted railway tracks in train circulation. Numerical simulations are a highly effective means of predicting track response and the propagation of vibrations to the free field. However, numerical simplifications often prevent these models from performing additional in-depth analyses of three-dimensional track response or non-linear behaviour of the track ballast and foundation soil. This thesis aims to expand the knowledge of ballasted railway track response by performing 3D non-linear railway track simulations and investigating the importance of non-linear material behaviour in numerical predictions. The first part of the thesis concentrates on the elastodynamics of railway track response to moving loads and the numerical accuracy of 3D Finite Element meshes of railway tracks. The advantages and disadvantages of 3D Finite Element simulations for these structures are highlighted and the cases for which they are suitable are identified. The second part of this thesis focuses on non-linear ballast and soil response using time-domain simulations. The study of ballast behaviour is performed using a constitutive model in which the separated consideration of yield surfaces and pressure dependent Young’s modulus, facilitates the identification of their individual influences on track response. The 3D nature of the model also enables the study of the stress and strain distribution in ballast, in the transversal and longitudinal directions of the track, which provide insight into the difference in behaviour between ballast under a sleeper and ballast between two sleepers. The evaluation of the non-linear soil response is conducted using a cyclic non-linear model that was implemented in the Finite Element software. This model examines the spatial distribution and time history of the stiffness degradation experienced by the soil during the passage of a train axle. Finally, the simulation of the integrated non-linear soil and ballast material models demonstrates the influence of non-linear behaviour at different circulation speeds.