An exact solution for the problem of vibration of a circular plate weakened along an internal concentric circle due to the presence of an angular crack, rotationally restrained and simply supported along an edge of the plate is derived. Frequencies for the first six modes of plate vibrations are computed for varying values of the elastic rotational edge restraint, radius of an angular crack and the extent of weakening duly simulated by considering an angular crack as an elastic rotational restraint on the plate. Internal weakening due to crack is found to cause decrease in fundamental frequency of the plate by around as high as 30%. Exact method of solution and the results presented in this paper are expected to be of specific use in analyzing the effect of an angular crack on fundamental frequency of the circular plate in the presence of a rotational restraint with simply supported boundary along the outer edge of the plate. These exact solutions can be of use in checking numerical or approximate results obtained through numerical methods such as finite element method © 2015 Springer Science+Business Media New York.