In order to analyze the effects of system stiffness on random response, a dynamic model and random motion differential equations are established. By using a pseudo excitation method based on a computer numerical simulation along with a power spectral density function, the casing elasticity and gyro torque are analyzed for the random response of the complex cantilever double-disc rotor system, with multi-parameter coupling random excitation, bearing slewing random dynamic excitation, rotor imbalance random excitation, ground earthquake random excitation, and other effects that system stiffness has on the random response. The analyses show that random response is relatively strong during an earthquake in the horizontal direction, and when the vibration of the disc with the cantilever end is strongest. Moreover, there is a greater impact on random response due to casing stiffness, casing joint stiffness, and bearing stiffness. It is thus advantageous to improve the stiffness of the system in order to reduce the random response. The results of the analyses show that it is appropriate to use the virtual excitation method to analyze the random response of the complex rotor system, which can provide the basis for selecting reasonable system parameters and controlling random vibration.