This article analyses the dispersion of vibration accelerations of a railway bridge during the passage of a train, and presents an analysis of their parameters after the application of the theory of covariance functions. The measurements of vibration accelerations at the fixed points of the beams of the overlay of the bridge were recorded in the time scale as digital arrays (matrices). The values of inter-covariance functions of the arrays of data of measurements of digital vibration accelerations and the values of auto-covariance functions of the individual arrays, changing the quantization interval in the time scale, were calculated. The compiled software Matlab 7 in the operator package environment was used in calculations. This article aims at determining the interdependencies of results of vibrations of bridge points rather than at the impact which a train makes on a bridge without emphasizing the modal parameters of the bridge. The aforementioned interdependencies make it possible to predict the results of hard-to-reach points.