Abstract: Abstract: Hydropower plant can be expected gradually undertake the task of peak shaving and frequency modulation in the power grid, in order to reduce the impact from the renewable energy, such as the solar, and wind energy. In the switch operating conditions of hydraulic turbines, it is a high demand to fully meet the grid requirements during power generation. Consequently, the turbine can be required to work at the off-design conditions, particularly with the high operation stability. This study aims to explore the flow and structure characteristics of Francis turbine under different conditions (0.35Qr, Qr, and 1.09Qr). The turbulence model of SST k-ω was used to solve the internal fluid, whereas the method of fluid-solid coupling was adopted in the structure field. There was the deviation between the relative velocity direction angle of flow and the inlet angle of blade at the off-design points, where the maximum eddy viscosity at 0.35Qr and 1.09Qr were 3.97 and 2.23 times of Qr, respectively. Some parameters were analyzed quantitatively, including the velocity, pressure, eddy viscosity, equivalent stress, and deformation extent. The results show that both Smax and dmax increased with the increasement of load. The large values of Smax appeared at the outlet edge of blade, which was close to the upper crown, whereas the dmax appeared in the middle region of blade outlet edge, under all three conditions. The axial vortex generated by the impact flow at the runner inlet was the main reason for the increment of eddy viscosity, equivalent stress, and deformation extent under off-design conditions, wherein the Smax at Qr is larger than that of 0.35 Qr and smaller than 1.09 Qr, respectively. Stress concentration occurred at the connection area between the blades and the crown, due to the strong constraint at the connection position, where deformation extent was small. However, the dmax appeared at the center position of blades that caused by the strong constraint of upper crown, In addition, the combination of theoretical analysis and numerical simulation was applied to investigate the runner performance, with the different manufacturing materials. The results illustrated that the frequency of Q345 runner at the wet modal shared the highest decrease rate. Among them, the maximum decreasing ratio was 24.5%, which frequency drop rate is bigger than that of ZG00Cr13Ni5Mo. Thus, the fluid damping effect should be fully considered, when using Q345, but Q345 was lighter form the aspect of weight. The critical speed of each material runner was much higher than the working speed of turbine. There was no resonance during this time. The critical speed of ZG00Cr13Ni5Mo runner was the lowest. The runner presented the strongest ability of deformation resistance, when it was made of Q345 and 1Cr18Ni9Ti materials. Therefore, the Q345 was more suitable for the runner manufacture. Moreover, there were the similar developments of static characteristics on the equivalent stress and deformation extent for runners with different materials. Furthermore, all runners with different materials showed the similar vibration modes. Hence, each material can be extended to the other common materials. This finding can provide some reference and guidance for the design and operation of hydraulic turbine.