Abstract: The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design of a slender rocket. The inherent inaccuracies existing in manufacturing, measurements, uncertainties of geometry and material, statistical variability of constraints and other factors, have remarkable effects on the dynamic performance of the rocket. In this paper, based on the transfer matrix method and perturbation method, a new method for random eigenvalue problems of a slender rocket with uncertain parameters is studied, and the effect of parameter uncertainty on the vibration characteristic of the rocket is presented. This method does not need the global dynamic equations of a system, and has the high computational efficiency and low memory requirement. It has more advantages for the dynamic design of an uncertain rocket. The random eigenvalue problems of a slender rocket with uncertain parameters are studied by using the proposed method and Monte Carlo method, respectively. The computational results obtained by the two methods have a good agreement, which validate the feasibility of the proposed method.