High-Speed Rail (HSR) as a fast, reliable and environmentally friendly mode of transportation has received a lot of attention in recent decades. The International Union of Railways reported that there are more than 18600 miles of HSR in operation and about 1.6 billion passengers per year are carried by them. Although there are plans for HSR in many states including Florida, the United States, however, is still hesitant to develop its own HSR network. One of the main barriers to developing high-speed rail is excessive vibration propagation to the media which may cause annoyance to people who live in the track neighborhood. Train induced vibration also contributes to track settlement, developing track flaws, and increasing life cycle cost of track and supporting structures. The aim of this research is to address this problem by conducting a comprehensive investigation into track dynamics. For this purpose, three-dimensional mass-spring-damper models of vehicle, track and supporting structures were developed and matrices of mass, stiffness, and damping of each subsystem were formed. The response of the whole system was, then, determined by coupling the subsystems using Hertz contact theory. The differential equations of the coupled system were solved by the Newmark integration method and the results including vertical and lateral displacements and forces were presented in the time domain. Since the purpose of this dissertation is to quantify the effect of track and vehicle condition on vibration level, rail defects were also taken into account and rail random irregularities for the vertical profile, Gauge, alignment and cross level (super elevation) were incorporated into a numerical solution. The results of the study show the effect of track and vehicle parameters on the response of the vehicle, track, and substructures. Since Florida and some other states in the United States are very prone to hurricanes, an investigation was conducted into the effect of wind speed on vehicle stability. For this purpose, a curved beam was modeled to consider the influence of track curvature, cant deficiency, wind speed and train speed simultaneously. The results from the study show the maximum allowable values of train speed and axle load for different wind speeds. The findings can be used to decide under what circumstances there is a risk of vehicle overturning and how to avoid it.