Creation of vibro-protective devices on rolling contact bearings is widely spread in transportation technology and seismic protection. In this work, mathematical modeling of the oscillation movements of the elastic plate will be considered. The equations of motion for elastic plate on vibration supports bounded by high-order rotation surfaces by the Ostrogradsky-Hamilton principle are obtained. The natural frequencies of elastic plate  are determined.

 It is established that the value of the natural frequencies of elastic plate decreases with increasing height and increases with the width of the bases. The ratio of the natural frequency of the second form to the natural frequency of the first form does not depend on the geometrical parameters of the plate.