Abstract: In a periodic structural system such as blades in a circumferentially closed packet on a disk of turbo-machinery, the natural frequencies of individual blades can be randomly different from one another. From this arises the problem of vibration analysis of a periodic structure with random parameters. There is lack of general method for solving the differential equations with random parameters. This paper describes a spectral approach for analyzing the vibration of a periodic structure with random parameters. Suppose the standard deviations of random structural parameters are small so that a perturbation method can be used to reduce the differential equation with several random parameters to several differential equations with one parameter and then these differential equations may be solved one by one. Suppose the spatial distributions of the random structural parameters are ergodic, and for concrete structure these distribution functions and their correlation functions can be determined by experiments. It is suggested in this paper to expand these spatial distribution functions of random parameters into Fourier Series. And then the relation between these Fourier coefficients and the correlation functions is esta- blished so that these Fourier coefficients can be determined by several ways. In this situation, these differential equations with random parameters can be solved. Thus natural frequencies of the structure are then obtained, and their standard deviations are estimated. Also, the expressions of natural modes are given, the orthogonality of natural modes is proved, and it is shown that the phase angles of natural modes are not arbitrary. Finally the special conditions of resonance of periodic structure with random parameters are discussed. It is shown that a violent resonance occurs when the number of harmonic of exciting force is equal to the number of nodal diameters of natural modes, and only a weak resonance appears when these two numbers are not equal. This phenomenon does not exist in the case of structures with homogeneous parameters. The standard deviations of amplitudes of weak resonance are estimated, Numerical examples show that the calculated results have the same order as the experimental results in literature.