Traffic congestion of highways in many countries around the world has led railways to become the most popular means of public transportation, which increased the demand for faster and heavier trains. High- speed trains and heavy train loads are normally accompanied with strong vibrations in the track-ground system, which increases the risk of train derailment and track damages. Therefore, to allow for safer and reliable operation of high-speed trains, an investigation into the behavior of ballasted railway track foundations subjected to train moving loads at various speeds is a subject of prime importance in design of railway tracks. In the current study, sophisticated three dimensional (3D) finite elements (FE) numerical modelling was developed to investigate the impact of train speed on the dynamic response of track-ground system. In addition, some factors of the track-ground system affecting the critical speed including the modulus and thickness of track subgrade and ballast materials, and amplitude of train loading were investigated. The results were analyzed and presented, and their practical implications were discussed.