The mechanism of oxidation of organic sulfides in aqueous solutions by hydrogen peroxide was investigated via ab initio calculations. Specifically, two reactions, hydrogen transfer of hydrogen peroxide to form water oxide and the oxidation of dimethyl sulfide (DMS) by hydrogen peroxide to form dimethyl sulfoxide, were studied as models of these processes in general. Solvent effects are included both via including explicitly water molecules and via the polarizable continuum model. The former was found to have a much more significant effect than the latter. When explicit water molecules are included, a mechanism different from those proposed in the literature was found. Specific interactions including hydrogen bonding with 2-3 water molecules can provide enough stabilization for the charge separation of the activation complex. The energy barrier of the oxidation of DMS by hydrogen peroxide was estimated to be 12.7 kcal/mol, within the experimental range of the oxidation of analogous compounds (10-20 kcal/mol). The major reaction coordinates of the reaction are the breaking of the O-O bond of H2O2 and the formation of the S-O bond, the transfer of hydrogen to the distal oxygen of hydrogen peroxide occurring after the system has passed the transition state. Reaction barriers of the hydrogen transfer of H2O2 are an average of 10 kcal/mol or higher than the reaction barriers of the oxidation of DMS. Therefore, a two-step oxidation mechanism in which, first, the transfer of a hydrogen atom occurs to form water oxide and, second, the transfer of oxygen to the substrate occurs is unlikely to be correct. Our proposed oxidation mechanism does not suggest a pH dependence of oxidation rate within a moderate range around neutral pH (i.e., under conditions in which hydronium and hydroxide ions do not participate directly in the reaction), and it agrees with experimental observations over moderate pH values. Also, without including a protonated solvent molecule, it has activation energies that correspond to measured activation energies.