This investigation deals with the vibration problem of a rotating shrouded bladed disc and with the dynamic stresses of blades and packets of turbine blades. The wave propagation technique in periodic structures is introduced into the finite element method to reduce the overall number of degrees of freedom. The application of wave propagation technique to discs, disc-blades and shrouded bladed disc results in a small size eigenvalue problem which is easily solved to obtain the frequencies and mode shapes of these assemblies under the effects of rotation, disc thickness variations, disc flexibility and other design parameters. The numerical integration is used to evaluate the integrals of the stiffness and mass matrices of the variable thickness discs. The influence of rotational speeds and other design parameters such as; pretwist angles and stagger angles on the free vibration characteristics of blades, curved beams and packets of blades is studied using finite element method. The results of the natural frequencies are compared with the experimental results and with the results of other investigators. The dynamic stresses of blades and packets of blades are derived from the eigenvectors obtained in the vibration study of these components. The effects of rotational speeds, pretwist angles, stagger angles and shrouding on the dynamic stresses are studied.