A thin circular plate with generally restrained periphery and weakened along an internal concentric circle due to a crack, is considered in this paper for studying its vibration characteristics. The frequency for first six modes of plate vibration is computed for varying values of radius of crack, elastic rotational and translational restraints, and the extent of weakening duly simulated by considering the crack as a rotational restraint on the plate. From the results obtained, it is observed that for a plate with translation and rotational restraints, the internal weakening decreases the fundamental frequency by around 31 per cent.