Abstract
The study is devoted to construction of a mathematical model of a slab of a ballastless base of a railway track, assembled from separate segments fastened together. Each rectangular segment is modeled by a transversely isotropic prestressed plate. An equation has been obtained that allows researchers to study the natural oscillation frequencies of a rectangular plate, which is especially important from the point of view of choosing a final design of a ballastless track for high-speed main lines. An important issue solved is damping of supporting structures and separation of frequencies of natural and forced oscillations over different intervals of the frequency spectrum. To solve the set tasks, the decomposition method was used, its efectiveness and relative simplicity were proved.