The paper presents the dynamic behaviour of three-layer annular plates with damaged facings. The plate is composed of thin laminated, fibre-reinforced composite facings and thicker, foam core. Failure of the plate facings is modelled as fibre or matrix cracks. The plate loaded in the plane of facings with quickly increasing radially compressed forces loses its dynamic stability. Evaluation of the critical state of the plate with failures was carried out using both analytical and numerical solutions. The comparison of results between plates with material properties treated as isotropic, quasi-isotropic and composite has been conducted. Presented tables and figures create the image of dynamic responses of examined composite plates with structure failures.