The dynamic behavior of cavitation and gas bubbles under negative pressure has been studied numerically to evaluate the effect of gas bubble injection into a liquid on the suppression of cavitation inception. In our previous studies, it was demonstrated by direct observation that cavitation occurs in liquid mercury when mechanical impacts are imposed, and this will cause cavitation damage in spallation neutron sources, in which liquid mercury is bombarded by a high-power proton beam. In the present paper, we describe numerical investigations of the dynamics of cavitation bubbles in liquid mercury using a multibubble model that takes into account the interaction of a cavitation bubble with preexisting gas bubbles through bubble-radiated pressure waves. The numerical results suggest that, if the mercury includes gas bubbles whose equilibrium radius is much larger than that of the cavitation bubble, the explosive expansion of the cavitation bubble (i.e., cavitation inception) is suppressed by the positive-pressure wave radiated by the injected bubbles, which decreases the magnitude of the negative pressure in the mercury.