Hydropower is a major renewable clean energy and is widely used worldwide. The reversible pump-turbine unit of the pumped-storage power station is able to work in two main operating modes as required by the power grid: turbine-mode for power generation and pump-mode for power storage. In order to absorb unstable energies such as wind and solar energy and improve the quality of the electricity, reversible pump-turbines need to frequently change operating conditions, and experience more start-stops under different operating modes in a short period. The unstable flow during these transient processes will lead to high-level stresses on the structural components of the pump-turbine units. Therefore, it is of great engineering and academic significance to study the flow characteristics and structural characteristics of the unit during the transient processes. This paper has established a numerical calculation model for a prototype reversible pump-turbine unit, has carried out the CFD calculations of the pump-turbine fluid domains during the pump shutdown transient process, and has analysed the corresponding structural dynamic characteristics of the stationary components of the unit with the fluid-structure coupling method. The pressure variation trend of the spiral case outlet during pump shutdown has the same trend as that of the spiral case domain, and the guide vane flow domain. The maximum flow-induced deformation and stress of the stationary structures have a strong correlation with the axial thrust values of the head cover. The maximum deformation occurs at the inner edge of the head cover, and the maximum stress appears in the fillet of the stay vane leading edge. An increase in the number of shutdowns will result in a higher real risk of fatigue damage to the stay vanes. The conclusions obtained are of great value for safe operation, field condition monitoring, fault diagnosis, and predictive maintenance of the pump-turbine units.