The effect of four general anesthetics, namely chloroform, halothane, diethyl ether, and enflurane on the free volume fraction and lateral pressure profiles in a fully hydrated dipalmitoylphosphatidylcholime (DPPC) membrane is investigated by means of computer simulation. In order to find changes that can be related to the molecular mechanism of anesthesia as well as its pressure reversal, the simulations are performed both at atmospheric and high (1000 bar) pressures. The obtained results show that the additional free volume occurring in the membrane is localized around the anesthetic molecules themselves. Correspondingly, the fraction of the free volume is increased in the outer of the two membrane regions (i.e., at the outer edge of the hydrocarbon phase) where anesthetic molecules prefer to stay in every case. As a consequence, the presence of anesthetics decreases the lateral pressure in the nearby region of the lipid chain ester groups, in which the anesthetic molecules themselves do not penetrate. Both of these changes, occurring upon introducing anesthetics in the membrane, are clearly reverted by the increase of the global pressure. These findings are in accordance both with the more than 60 years old "critical volume hypothesis" of Mullins, and with the more recent "lateral pressure hypothesis" of Cantor. Our results suggest that if anesthesia is indeed caused by conformational changes of certain membrane-bound proteins, induced by changes in the lateral pressure profile, as proposed by Cantor, the relevant conformational changes are expected to occur in the membrane region where the ester groups are located.