Abstract: The vibration characteristics and structural stiffness of the gate leaf and side-wheel assembly of a rapid gate directly affect the operational reliability of hydropower units. In this study, finite element modal analysis was used to assess mesh convergence across multiple mesh sizes and to calculate the natural frequencies of the gate leaf and side-wheel assembly. The influence of mesh size on the modal analysis results was investigated, and the strain distribution of the gate leaf under different water pressures was analyzed. The results show that the modal frequencies of the gate leaf are insensitive to mesh size, and a mesh size of 0.05 m is recommended for subsequent calculations. In contrast, the side-wheel assembly exhibits high mesh sensitivity. Only the fine mesh with a size of 0.005 m can accurately capture the seventh mode (532.81 Hz) and avoid stiffness distortion. The baffle of the hoisting mechanism is the primary resonance-prone area of the gate leaf, where resonance is likely to occur under excitation at 8 Hz or at frequencies of 19 Hz and above. Under high-frequency excitation, most deformation occurs at the side-wheel support base, and prolonged operation can accelerate bearing wear and increase the risk of structural instability. Strain in the gate leaf increases linearly with water pressure and is concentrated around the baffle connections. The intersections of the grid-pattern longitudinal girders and the main transverse girder exhibit very low strain, demonstrating that the gate leaf structure has high stiffness and good resistance to deformation. The findings provide a theoretical basis for vibration-resistant design, identification of vulnerable areas, and maintenance scheduling for rapid gates.