It is well established that higher train speeds can amplify dynamic forces exerted on the track and ground surface. This effect becomes particularly pronounced under high-speed operations. Research indicates that when train speeds approach or exceed certain critical thresholds, surface waves generated by high-speed trains can induce severe vibrations in the track structure. To investigate the underlying mechanisms of these vibrations, this chapter employs an analytical approach for dynamic analysis of the track structure. A continuous elastic foundation beam model is developed to simulate the track system, examining the characteristics of ground waves induced by high-speed trains and their contribution to track vibrations. Additionally, the influence of track stiffness on critical speed and vibration response is systematically analyzed using this analytical method.