We report results on the pressure effects on hydrophobic interactions obtained from molecular dynamics simulations of aqueous solutions of methanes in water. A wide range of pressures that is relevant to pressure denaturation of proteins is investigated. The characteristic features of water-mediated interactions between hydrophobic solutes are found to be pressure-dependent. In particular, with increasing pressure we find that (1) the solvent-separated configurations in the solute-solute potential of mean force (PMF) are stabilized with respect to the contact configurations; (2) the desolvation barrier increases monotonically with respect to both contact and solvent-separated configurations; (3) the locations of the minima and the barrier move toward shorter separations; and (4) pressure effects are considerably amplified for larger hydrophobic solutes. Together, these observations lend strong support to the picture of the pressure denaturation process proposed previously by Hummer et al. (Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1552): with increasing pressure, the transfer of water into protein interior becomes key to the pressure denaturation process, leading to-the dissociation of close hydrophobic contacts and subsequent swelling of the hydrophobic protein interior through insertions of water molecules. The pressure dependence of the PMF between larger hydrophobic solutes shows that pressure effects on the interaction between hydrophobic amino acids may be considerably amplified compared to those on the methane-methane PMF.