As a result of their inherent planarity, DNA base radicals generated by one-electron oxidation/reduction or bond cleavage form π- or σ-radicals. While most DNA base systems form π-radicals, there are a number of nucleobase analogues such as one-electron-oxidized 6-azauraci1, 6-azacytosine, and 2-thiothymine or one-electron reduced 5-bromouracil that form more reactive σ-radicals. Elucidating the availability of these states within DNA, base radical electronic structure is important to the understanding of the reactivity of DNA base radicals in different environments. In this work, we address this question by the calculation of the relative energies of π- and σ-radical states in DNA/RNA bases and their analogues. We used density functional theory B3LYP/6-31++G** method to optimize the geometries of π- and σ-radicals in Cs symmetry (i.e., planar) in the gas phase and in solution using the polarized continuum model (PCM). The calculations predict that σ- and π-radical states in one-electron-oxidized bases of thymine, T(N3-H)(•), and uracil, U(N3-H)(•), are very close in energy; i.e., the π-radical is only ca. 4 kcal/mol more stable than the σ-radical. For the one-electron-oxidized radicals of cytosine, C(•+), C(N4-H)(•), adenine, A(•+), A(N6-H)(•), and guanine, G(•+), G(N2-H)(•), G(N1-H)(•), the π-radicals are ca. 16-41 kcal/mol more stable than their corresponding σ-radicals. Inclusion of solvent (PCM) is found to stabilize the π- over σ-radical of each of the systems. U(N3-H)(•) with three discrete water molecules in the gas phase is found to form a three-electron σ bond between the N3 atom of uracil and the O atom of a water molecule, but on inclusion of full solvation and discrete hydration, the π-radical remains most stable.