The transverse vibration of flexible, uniform and variable thickness discs is investigated theoretically by using the Ritz method and the finite element technique, and experimentally by applying the technique of holographic interferometry. The theoretical analysis is developed by the Ritz approach with use of up to five terms of a functional series. A thin, twodimensional annular sector element with 12 degrees of freedom is also developed for the disc. A thick, three-dimensional cylindrical element is developed including the effect of rotary inertia and shear deformation on the dynamic analysis of uniform and variable thickness discs. The triple integration for stiffness and mass matrices is carried out numerically by applying Gaussian quadrature using a (4 \times 4 \times 4) mesh. The advantages of cyclic symmetry of the wave propagation technique are fully utilized in the finite element analysis. The large sizes of the stiffness and mass matrices, obtained in the case of a three-dimensional element analysis, are reduced by using the eigenvalue economizer technique. The experimental results obtained by using the time-average holographic technique show very good agreement with the theoretical results.