A general multi-body formulation to analyze the tolerance effects on the statistical property variations of natural frequencies of multi-body systems undergoing constant rotational motion is proposed in this paper. To obtain the tolerance effects, Monte-Carlo simulation method is conventionally employed. However, the Monte-Carlo simulation has serious drawbacks; spending too much computation time for the simulation and achieving very slow convergence around some dynamically unstable regions. To resolve such problems, a method employing analytical sensitivity information is suggested in this paper. To obtain the sensitivities of natural frequencies the eigenvalue problem should be differentiated with respect to a design variable. The sensitivities of mass and stiffness matrices should be calculated at the dynamic equilibrium. By employing the sensitivities of natural frequencies along with the tolerance of the design variable, the statistical property variations of the natural frequencies can be calculated.