Mass and stiffness matrices of an annular element consisting of base plate and unconstrained damping layer have been derived assuming a modal solution to the equation of motion of the plate. The complex eigen equations have been solved for frequencies and loss factors by an extension of the simultaneous iteration technique. Frequencies of unlayered plates and loss factors of fully layered plates have been compared with those available in literature. The effect of staggering of layers on the vibration characteristics of the plate has been investigated. It is found that when the plate is partially layered starting from its inner edge the loss factors will be higher for all boundary conditions and modes than when the plate is fully layered provided the mass of the damping layer is kept the same in both cases. © 1986.