The elastic cushion is mostly used between the layers of ballastless tracks laid on a large-span cable-stayed bridge with a main span of more than 300 m. The rubber material is easy to harden and age, the geotextile has good acid-alkali resistance and antiwear performance, and the feasibility of geotextile application on the large-span cable-stayed bridge can be explored. The coupling model of a long-span cable-stayed bridge and the ballastless track was established to analyze the longitudinal mechanical characteristics of the seamless line, the deformation of the track structure, and the separation of the track plate and base plate under different loads. The results show that the application of geotextile or elastic cushion has little effect on the longitudinal mechanical properties of seamless lines. Compared to the elastic cushion, laying the geotextile increases the longitudinal stress of the slab by 0.13 Mpa, 0.025 Mpa, and 0.06 Mpa under different types of loads. The strength calculation of the seamless track is within the safety range. Laying elastic cushion can restrain the generation of separation under vertical loads, but there is no effect laying elastic cushion under temperature loads and braking loads, and the height of separation was less than 0.4 mm. The stress and deformation of the ballastless track do not exceed the standard when applying geotextile; it is feasible to apply geotextile on ballastless tracks on a large-span cable-stayed bridge. The next step is to study the vehicle–bridge–track dynamic response when elastic cushion and geotextile are laid.