The vibration problem is prominent in pumped storage power stations, and strong vibrations can seriously affect the safe and stable operation of power units and plants. This study employed viscoelastic artificial boundaries to simulate the boundary conditions at the connection parts between the plant and surrounding rock. Firstly, the natural frequency characteristics of the whole underground plant structure of a unit in Fengning Pumped Storage Power Station was calculated and analyzed, the resonance checks of which were then conducted. Subsequently, the time-history method was used to calculate and analyze the vibration responses of the plant structure under pulsation pressure, after which the calculation results were compared with the measured data. The results show that the first 20 natural frequencies of the whole plant structure range from 13.32 to 34.90 Hz, indicating a very low risk of structure resonance. There is little difference between the calculated value and measured value of the vertical root-mean-squared acceleration at each measuring point of the floors, which indicates that the numerical analysis method is reasonable and effective. In addition, the maximum vibration response of each typical part of the structure meets the vibration control standard of the plant under pumping condition. Except that the maximum vertical root-mean-square acceleration of the turbine floor exceeds the human health evaluation standard, all the indexes of the other structures meet the vibration control standard of the plant under power generation condition.