In the articles of Bkhadeshia, a new class of high-strength steels based on the structure of carbidefree bainite with an enhanced carbon content has been developed. According to Bkhadeshia, the main factor responsible for the high solubility of carbon is the occurrence of a tetragonality of the bainite lattice. To check this effect, in this article, the theory of tetragonality of martensite of iron alloys developed by Zener and Khachaturyan was applied to bainite under the assumption that the precipitation of carbides is prohibited. Equations for the chemical potentials of carbon and iron in austenite and in tetragonal ferrite have been derived. The equilibrium of these phases has been considered, and the calculations of the boundary concentrations of carbon and iron at different temperatures (300–1000 K) and at different parameters of the deformation interaction λ0 have been performed. The rigorous calculations confirmed Bkhadeshia’s hypothesis that the suppression of the carbide formation during the formation of bainite leads to an increase in the carbon solubility in the bcc phase.