Abstract: An efficient analysis method is proposed for rotating shaft systems with uncertain parameters subjected to stationary random seismic excitations. The pseudo excitation method is first used to transform the random excitations into deterministic sinusoidal excitations. As a result, the dual-random problems are transformed into much simpler single excitation problems accurately, which can be computed using the conventional perturbation method. Numerical examples show that the results computed using the proposed method agree well with those obtained from Monte-Carlo simulation.