Abstract: Tsunami waves induced by submarine volcanic eruption involve multi-source mechanisms, such as underwater explosions, pyroclastic flows, flank failures, column and caldera collapses, and atmospheric pressure disturbances. Based on the cylindrical Boussinesq equations, a numerical model for tsunami waves driven by axisymmetric motion of atmospheric pressure disturbances is developed to understand how axisymmetric pressure fields lead to tsunami waves and explore how pressure parameters affect water wave patterns. The accuracy and stability of the present model are verified against numerical results of cylindrical wave propagation on different terrains. Furthermore, a numerical simulation of the 2022 Tonga volcanic tsunami event is implemented. The computed wave elevations induced by the atmospheric pressure disturbance from the volcanic eruption agree well with the DART buoy data in the Pacific ocean, which demonstrates the air-water coupling mechanism for the generation and propagation of Tonga tsunamis. The dispersion behavior of tsunami waves in certain regions of the deep ocean is discussed. The effects of the radial velocity, spatial scale, and strength of the pressure disturbance are studied. It turns out that the water wave pattern is strongly related to the radial velocity of pressure. The Proudman resonance is triggered when the pressure velocity approaches the long wave celerity, and the amplitude of the resonant wave grows approximately linearly with respect to radial propagation distance. The amplitude amplification factor decreases with the increase of pressure scale under the resonance condition, while the influence of pressure strength is negligible. In contrast, apart from the resonance condition, there is less influence of both the spatial scale and the strength of the pressure disturbance on the amplitude amplification factor, and the cylindrical free wave amplitude decays with distance due to the wave energy conservation, while the forced wave amplitude varies according to the decay law of pressure disturbances.