In the high-speed transportation sector, magnetic levitation (maglev) technology has numerous advantages, including, first and foremost, the contactless motion of the vehicle along the track, which allows significantly higher speeds than the wheel-on-rail system of classical railroad trains. At the same time, a maglev system is undoubtedly preferable to air travel in terms of energy requirements and environmental protection. Against the background of recent plans in China to develop a new 600~km/h high-speed maglev train, this dissertation deals with the mechanical modeling and numerical simulation of the dynamics of high-speed maglev trains, which, like the \tr{}, are based on the electromagnetic suspension principle. With the development of suitable simulation models of the coupled vehicle-guideway system using the elastic multibody systems approach, this dissertation makes a valuable contribution to the simulation-based development process of future high-speed maglev trains. In addition to modeling, it contributes to technological progress with simulative investigations gaining insights into various aspects of coupled vehicle-guideway dynamics. A rigid multibody vehicle model is coupled with an elastic guideway by moving forces in a two-dimensional longitudinal-section model, implementing an infinitely long elastic guideway. For numerous questions, two-dimensional models are sufficient and even desirable to keep the model complexity and the computation times low. Some aspects of interest, however, require a three-dimensional model, such as magnet failure scenarios or driving along curves. To allow for investigating those issues, the last part of the dissertation focuses on developing a comprehensive three-dimensional model of one single vehicle section.