Abstract: Parameter uncertainty of structural systems is inherentin most engineering problems. It is necessary to study thereliability of uncertain systems. Frequency analysisis important for reliability study of dynamically uncertainstructures. In this paper, the criterion is used that the differencebetween the natural frequency anddriving frequency should be less than a specific value. The reliability mode and the safetyprobability of the random axial vibration systems of rods are definedas a series mode, and the frequency reliability analysis method foravoiding the resonanse is proposed. The quasi-failure analysis methodfor resonant problem of the random axial vibration systems of rods isstudied.