The stabilities of the adducts deriving from H free radical addition to the O2, O4, and C5 positions of 3'-uridine monophosphate (3'UMP) are studied by the hybrid density functional B3LYP approach. Upon H atom addition at the O2 position, a concerted low-barrier proton-transfer process will initially occur, followed by the potential ruptures of the N-glycosidic or beta-phosphate bonds. The rupture barriers are strongly influenced by the rotational configuration of the phosphate group at the 3' terminal, and are influenced by bulk solvation effects. The O4-H adduct has the highest thermal stability, as the localization of the unpaired electron does not enable cleavage of either the C1'-N1 or the C3'-O(P) bonds. For the most stable adduct, with H atom added to the C5 position, the rate-controlled step is the H2'a abstraction by the C6 radical site, after which the subsequent strand rupture reactions proceed with low barriers. The main unpaired electron densities are presented for the transient species. Combined with previous results, it is concluded that the H atom adducts are more facile to drive the strand scission rather than N-glycosidic bond ruptures within the nucleic acid bases.