In this study, the natural frequencies of annular plates with circumferential cracks are investigated by using finite element method. The cracks were non-propagating and open. In the event of the selection of appropriate half sector angle, taking into account the closeness of the geometries of the sector and trapezoidal element, the flexibility matrix of the sector element with crack was obtained by the flexibility matrix of the trapezoidal element. Also, because of small half sector angles, the circumferential cracks in the elements were assumed to be straight cracks. The results of this study with improved elements are compared with the theoretical results in the literature. It is observed that the location and the number of cracks have various effects on the natural frequencies related to the vibration modes. (c) 2007 Published by Elsevier Ltd.