In order to investigate the influence of stochastic factors on dynamic characteristics, a universal grey number-based approach was used to carry out the solute on to natural frequencies of uncertain chain structures. Based on the analysis of four arithmetic operations of the universal grey numbers, this paper presents an improved division operation for the universal grey number and discusses some drawbacks of this method for interval analysis. Based on the transfer matrix method, a nonlinear universal grey number based equation of natural frequencies was obtained using universal grey mathematics. Subsequently, a forward and backward searching algorithm was presented to solve the equation. The feasibility and effectiveness of the computation expressions derived in this paper were confirmed through special cases.