Abstract: Stathtical properties of the dynamic characteristics of structures, including the random parameters , are studied by the opelator method. Random characteristics of structural parameters are taken as random perturbation around the mean value.Variations to Rayleigh's quotient of the eigenvalue of vibration for elastic structures are performed Perturbation formula of the structural dynamic characteristics can be obtained, leading to easily the concept of structural dynamic sensitivity, and arriving at the statistical formula for the structural dynamic charactristics. An illustrative example is finally given.