Density functional methods, alone and together with molecular mechanics, are used to study the catalytic mechanism of galactose oxidase. This enzyme catalyzes the conversion of primary alcohols to the corresponding aldehydes, coupled with reduction of dioxygen to hydrogen peroxide. It is shown that the proposed mechanism for this enzyme is energetically feasible. In particular the barrier for the postulated rate-limiting hydrogen atom transfer between the substrate and the tyrosyl radical, located at equatorial Tyr272, is very plausible. We propose that the radical site, prior to the initial proton transfer step, is located at the axial tyrosine (Tyr495). The radical is transferred to the equatorial tyrosine (Tyr272) simultaneously with the proton transfer. It is, furthermore, argued that the electron transfer from the ketyl radical intermediate to Cu(II) cannot be very exothermic, because this would render the oxygen reduction steps rate-limiting. Finally, the cysteine cross-link on the active site tyrosine is shown to have very minor effects on the energetics of the reaction.