Computer simulations of bubble oscillations are performed for various ambient pressures in order to study the mechanism of the ambient-pressure dependence of sonochemical reactions: sonochemiluminescence of aqueous luminol solutions [T. Tuziuti et al., J. Chem. Phys. 116, 6221 (2002)] and the oxidation of iodide [A. Henglein et al., J. Phys. Chem. 97, 158 (1993)]. It is shown that for air bubbles there exists an optimal bubble temperature for the production of the oxidants such as O, OH, H2O2, and O-3 inside bubbles regardless of the ambient pressure because at higher bubble temperature the oxidants are consumed inside bubbles by oxidizing nitrogen. Correspondingly there exists an optimal acoustic amplitude for each ambient pressure, which shifts toward a lower value as the ambient pressure decreases because bubbles expand more. It results in the higher rate of sonochemical reactions for lower ambient pressure at relatively low acoustic amplitude. For oxygen bubbles, the amount of the oxidants created inside bubbles is larger for higher bubble temperature because in this case the oxidants are not consumed inside bubbles due to the absence of nitrogen. Regardless of the species of the gas inside bubbles, the decrease of the ambient pressure works as if the acoustic amplitude increases because bubbles expand more. (C) 2003 American Institute of Physics.