Railway tracks are subjected to heavy repeated loads due to the train traffic. These loads can damage the track and especially its supports. To compute the behavior of railway tracks, many authors used a periodicity hypothesis, which is broken by the presence of a damaged zone. Researchers proposed different analytical or numerical methods to compute the dynamics of such structures. Analytical methods permit low numerical cost computations of the track dynamics, but are limited to very simple representations of the track, whereas numerical methods allow the use of much more detailed representations of the track but with higher numerical cost. In most regions, railway tracks can be modeled as periodic structures. Several methods take advantage of this periodicity to limit the numerical cost for the computation of the track dynamics. Among these methods, the Wave Finite Element (WFE) method was initially created to compute free vibrations in periodic structure. This method was improved to compute the dynamic response of periodic structures subjected to any kind of loads. In recent development, the authors adapted the WFE method to compute the response of structure composed of two semi infinite periodic zones linked by a central zone with different mechanical properties. In this paper, the results obtained with an analytical method will be compared to results obtained with the WFE method for the computation of the dynamic responses of different ballastless railway tracks such as healthy, damaged tracks. In these computations, the tracks will be subjected to constant moving load representing the load applied by a train wheel. In the WFE results, the rail, the supports, and the supporting concrete slabs are represented with a three-dimensional model. A special focus will be made on the state of stress of the different materials which constitute the tracks. A failure criterion will be computed at components scale for the different tracks simulated. This criterion can then be used to compute the likeliness of long-term fatigue of the track components.