Reaction mechanisms for helium incorporation into C-60 have been examined by semiempirical (MNDO), ab initio (HF/3-21G), and density functional (BLYP/3-21G, BP86/3-21G) calculations. Effective activation barriers for the penetration through an intact cage and for the insertion through the two possible one-bond windows and six different two-bond windows are reported both in the lowest singlet and triplet state. The computed barriers are very high and exceed 200 kcal/mol for each of the 21 pathways considered. These results require a new mechanistic interpretation of the high-pressure experiments where helium incorporation into fullerenes is observed under thermal conditions. Mechanistic alternatives are discussed including the possible role of imperfect C-60 isomers and other intermediates.