Based on the Timosheko beam theory, the stochastic finite element of a rotating shaft was proposed for the rotor system modelling in which material and geometric random properties were described as one dimensional stochastic field functions. The random response analysis method was developed in order to determine the statistics of dynamic responses of stochastic rotor systems under random loads. A linear and a nonlinear turbopump rotor systems were employed to compare the results obtained by the proposed mode, method and Monte Carlo simulation. And the numerical results, which coincide well with Monte Carlo simulation data, demonstrate that the proposed stochastic model and method are feasible and efficient in actual rotor system analysis and design.