Cracks that develop on machine members and structures influence their dynamic behavior. The Rayleigh principle is used for an estimation of the change in the natural frequencies and modes of vibation of the structure if the crack geometry is known, assuming that the eigenvalue problem for the uncracked structure has been solved in advance. The method reduces the computational effort needed for the full eigensolution of cracked structures and gives acceptable accuracy. It can be extended to higher modes and to decompose degenerate modes found in symmetric structures. To demonstrate the change in the dynamic behavior of linear structures with the crack depth, a cylindrical shaft and a plane frame consisting of prismatic bars were analyzed for dynamic sensitivity to surface cracks.