The excitation frequency approaches the natural frequency of the system in a vibration system, which will induce significant dynamic risk. Moreover, many vibration systems exhibit inherent uncertainties, whereby minor parameter variations can elicit substantial effects on the system’s dynamic response. Accounting for the stochastic uncertainties of individual parameters, this study employs the Jeffcott rotor as a case study and utilizes the polynomial chaos expansion (PCE) method to develop a metamodel for the natural frequency of the system in the frequency domain. Using the developed metamodel, the statistical moments and probability distributions of the natural frequency are analyzed. The reliability criteria and failure modes for the Jeffcott rotor resonance problem are defined. Leveraging the statistical moments and probability distributions of the natural frequency of the system, the parameter sensitivity of the Jeffcott rotor resonance problem is investigated through the integration of the theory of complex mode, reliability theory, and sensitivity analysis methodologies. The proposed framework in this study offers a theoretical foundation for parameter design in rotor systems with stochastic parameters.