A mechanism of general anesthesia is suggested and investigated using lattice statistical thermodynamics. Bilayer membranes are characterized by large lateral stresses that vary with depth within the membrane. Incorporation of amphiphilic and other interfacially active solutes into the bilayer is predicted to increase the lateral pressure selectively near the aqueous interfaces, compensated by decreased lateral pressure toward the center of the bilayer. General anesthesia likely involves inhibition of the opening of the ion channel in a postsynaptic ligand-gated membrane protein. If channel opening increases the cross-sectional area of the protein more near the aqueous interface than in the middle of the bilayer, then the anesthetic-induced increase in lateral pressure near the interface will shift the protein conformational equilibrium to favor the closed state, since channel opening will require greater work against this higher pressure. This hypothesis provides a truly mechanistic and thermodynamic understanding of anesthesia, not just correlations of potency with structural or thermodynamic properties. Calculations yield qualitative agreement with anesthetic potency at clinical anesthetic membrane concentrations and predict the alkanol cutoff and anomalously low potencies of strongly hydrophobic molecules with little or no attraction for the aqueous interface, such as perfluorocarbons.