There appears to be little published work on the flexural vibrations of a cut thin ring apart from a recent paper by H. Hasseigruber (1) who used the Rayleigh—Ritz method to find the frequency and shape of the first three modes. In the present paper these vibrations are investigated using exact methods, and tabulations are given for the first ten modes of symmetrical and anti-symmetrical vibration. There is no difficulty in extending the method to treat many problems of the flexural vibrations of circular arcs.