With the criterion that the absolute value of the difference between the natural frequency and forcing frequency, the frequency reliability analysis method of avoiding resonance and reliability model are proposed by the mechanical dynamics and reliability theory in the paper. Furthermore, the frequency reliability sensitivity analysis method is presented and the formulas of frequency reliability sensitivity for resonant problems of random structures are obtained using the sensitivity method, which is based on the frequency reliability and provide a preliminary efficient way to analyze how each random parameter contribute to the system reliability, moreover a numerical example of random bending vibration systems of continuous bars is provided, combining theory method and engineering practice, the frequency reliability and sensitivity numerical results are obtained, which are in agreement with practice and demonstrate the effectiveness and accuracy of the proposed method.