Pterins are naturally occurring pigments and enzyme cofactors widespread in living organisms. Tetrahydrobiopterin (H4Bip) is a coenzyme of aromatic amino acid hydroxylases, NO-synthases, and alkylglycerol monooxygenases. This coenzyme is prone to oxidation in the presence of molecular oxygen, a so-called autoxidation. The reactions participating in H4Bip autoxidation are well known. However, our study is an attempt to evaluate theoretically the feasibility of reactions participating in autoxidation. To do so, we have calculated the Gibbs free energy of elementary reactions between H4Bip, its derivatives, molecular oxygen, and reactive oxygen species (ROS). In the last few years, we have established the photosensitized oxidation of H4Bip experimentally. Thus, we have also evaluated the feasibility of H4Bip photooxidation reactions, which may occur according to both type-I and type-II photosensitized oxidation. We calculated Fukui indices for H4Bip and found particular atoms in the molecule that interact with nucleophiles (for example, singlet oxygen 1O2) and radicals (in particular, molecular oxygen 3O2). Therefore, we evaluated the probability of H4Bip autoxidation reactions, photooxidation reactions, and the reactivity of particular atoms in H4Bip molecule using the theoretical methods of quantum chemistry.