To investigate the three-dimensional resonant sloshing characteristics of free surface in a vertical cylindrical tank, a combined approach employing model experiments and smoothed particle hydrodynamics (SPH) was adopted. The accuracy of the SPH numerical model was validated through experimental data, and both experimental and numerical methods were employed to examine the impact pressure characteristics on tank walls under different external excitation parameters. Results indicate that the modal responses of the free surface are governed by both excitation frequency and amplitude. Increasing the excitation amplitude significantly expands the frequency response ranges of chaotic rotational waves and stable rotational waves. The impact pressure exhibits a nonlinear positive correlation with the excitation amplitude. Compared to planar wave modes, rotational motions (particularly chaotic rotational waves) generate substantially higher transient impact loads on the tank walls. Notably, the pressure time-history curves of chaotic rotational waves fail to reach steady-state responses and demonstrate stronger impact pressures than stable rotational waves. These findings provide critical insights for evaluating sloshing-induced loads in the design of marine vertical cylindrical liquid tanks.