Potential energy surfaces for the process of phosphonylation of the catalytic triad of acetylcholinesterase by sarin have been explored at the B3LYP/6-311G(d,p) level of theory through a computational study. It is concluded that the phosphonylation process involves a critical addition-elimination mechanism. The first nucleophilic addition process is the rate-determining step. The following elimination process of the fluoride ion comprises a composite reaction that includes several steps, and it occurs rapidly by comparison with the rate-determining step. The mobility characteristics of histidine play an important role in the reaction. A double proton-transfer mechanism is proposed for the catalytic triad during the phosphonylation process of sarin on AChE. The effect of aqueous solvation has been considered via the polarizable continuum model (PCM). One concludes that the energy barriers are generally lowered in solvent, compared to the gas-phase reactions.