Heavy-duty, oil-cooled brake discs (MMOTs) are often used in heavy-duty brake systems manufactured by companies such as Caterpilar, Clark, Komatsu and Liebherr. These discs are usually made of special steels, and in most cases, the flatness of the working surfaces should not exceed 0.15–0.30 mm. Although the technological processes of friction disc production include several stages of heat treatment and grinding, the required accuracy is not achieved in some cases. In addition, the remaining residual stresses lead to the deformation of the discs during their lifetime. In production practice, three methods are used to reduce residual stresses: thermo-fixing, dynamic stabilisation and vibratory stabilisation consisting in bringing discs to transverse resonance vibrations and maintaining resonance until significant stress reduction. The article proposes a method of stabilising the discs using the resonance phenomenon at the first few frequencies. In this article, Cauchy’s function method and characteristic series method are used to develop solution value problem for clamped circular plates with discrete inclusions as concentrated masses and springs. Calculation methods for quick estimation of the own frequency of discs with additional ring mass enabling the use of low power vibration inductors are presented. The use of a special membrane and a pneumatic cushion in the construction of the stand allows to induce vibrations of higher frequencies.