Abstract: The gas inside the underwater explosion bubble is assumed to undergo adiabatic expansion and compression. The water flow induced is assumed to be inviscid, irrotational and incompressible, which is simulated based on potential flow theory coupled with the boundary element method (BEM). Much attention was paid to the character of the pulsating pressure and the flow velocity, and the related theory and numerical method were given in detail. The validity and convergence of numerical model were confirmed by comparing the calculations with experimental and analytical results, so our BEM codes were used to simulate underwater explosion bubbles under different conditions. During the expansion phase of the bubble, the fluid pressure along the radius direction may first increase and then decrease. To simulate the subsequent motion after the bubble jet impact, a vortex ring was put inside the bubble, thus the flow field could be decomposed into two parts: an irrotational flow field and a vortex field. Besides, some numerical techniques were adopted to handle the topology of the bubble which made it possible to simulate multi-oscillations of bubbles. It's noted that there were two high-pressure regions formed around the top and the bottom of the toroidal bubble while its fast rise proceeded. It can also be found that the top region had a greater peak value, while the bottom region covered a larger area. Meanwhile, the flow velocity in the jet direction accelerated inside the toroidal bubble, but decelerated rapidly near the top of the bubble.