When a train is moving along the tracks, it is exposed to perturbations in the form of vertical and horizontal irregularities of the right and left rails causing oscillations in the mechanical parts of the rolling stock. This raises the problem of generating a multidimensional stochastic process of disturbances in accordance with a given matrix of auto-correlation and cross-correlation functions or spectral densities. For this purpose, the forming mechanism in the temporary realm was designed. This mechanism allows generating multidimensional stochastic processes of irregularity at different speeds for any length of implementation or discretization step in the temporary realm.