The results of the experimental and theoretical researches of slope stability of railway embankments are presented in the paper. The conclusions of criteria of similarity for modeling of the serviceability of railway embankments on geotechnical centrifuges under the vibro-dynamical loads from a train. In the paper the basic ways of reinforcement and stabilization of potentially-dangerous and deforming embankments of railways are shown, requirements to which are developed on the basis of results of centrifugal modeling of slope stability of a range of embankments, both on real prototypes, and on the basis of development of the generalized parameters of embankments according to the statistical data of the railway network of the Russian Federation.