The structures of C1, C2, C3, and C4 centered deoxyribose radicals are optimized at the UHF/6-31G level. For each radical two puckered conformations are observed, which are significantly different from those of deoxyribose. In C1 and C2 radicals the pseudorotation angle, P, is shifted toward higher values compared to that of deoxyribose. In C3 and C4 radicals the shift of P is in the opposite direction. In addition, the puckering amplitude tau(m) is significantly decreased in the radicals, indicating a flattening of the five-membered ring. The C2 centered radical has the sp2-type electronic structure, while C1, C3, and C4 centered radicals are pyramidal. The enthalpies for H-atom abstraction from deoxyribose are calculated at the MP2/6-31G* level including ZPE and a scaling of correlation energy. The abstractions from C1, C3, and C4 positions require similar energies, whereas the abstraction from the C2 carbon of deoxyribose is less favorable by 3-4 kcal/mol. The susceptibility of different deoxyribose hydrogens for abstraction is estimated on the basis of their bond strength and their accessibility in nucleotides and in DNA.