A mathematical model is presented for the slide as a continuous system along which a moving force from the capsule moves, and the capsule as a discrete system. The displacements of the magnet elements were determined by performing simulations. Simulations were carried out with ANSYS software using FEM (Finite Element Method) calculations. The results will determine the nature of the capsule's movement. The results of the simulations were used to study stability in a technical and stochastic sense (Lyapunov criterion) for non-linear systems, taking into account the conditions present in the magnet and guide element system. Transverse displacements of the electromagnets were used in the technical stochastic stability study. The paper also presents a method for determining technical and stochastic stability for the Hyperloop vehicle for different speeds and taking into account the displacements of the levitation set. The probability of unsteady Hyperloop motion was then determined.