Friction-induced vibration emanating from aircraft braking system is a key issue in the design phase, due to the significant damage it can cause to the brake structure. Although the problem of unstable vibrations in aircraft braking systems has been studied by a number of researchers, the suitability of the mechanical modeling strategy for predicting instabilities remains an open problem. The need for relevant numerical models is therefore essential in order to be as predictive as possible during the design phase. Preliminary studies must therefore be carried out to validate or invalidate the modeling hypotheses traditionally used. Indeed the stability analysis of an aircraft braking system is performed in order to study a low-frequency instability. An industrial model is used, hence reducing the number of degrees of freedom (DoF) is of utmost importance in order to have reasonable computation times. When studying low-frequency phenomena, this can be achieved by neglecting the deformations of the disks. However, no current study has shown that this hypothesis is realistic. So the aim of this paper is to assess the effect of the rigidity hypothesis on the results predicted by the stability analysis. In order to do so, the stability analysis results of a model with rigid disks and one with non-rigid disks are compared, with a particular attention on the main instability phenomenon. It is found that considering rigid disks has a very limited influence on the frequency of the low-frequency eigenmodes, but it over-predicts the real part of the unstable eigenmode. Besides, a component mode synthesis (CMS) technique is shown to reduce significantly the size of the non-rigid disks model while ensuring a satisfying precision regarding eigenmodes prediction.