We have analyzed by means of DFT calculations in conjunction with all-electron DGDZVP basis sets the thermodynamics of alkane free-radical iodination. The thermodynamic analysis of the radical iodination of some saturated hydrocarbons by t-butyl hypoiodite in the gas phase and solution with the use of the B3LYP/DGDZVP was carried out. The DFT calculations make predictions about the thermodynamic probability of the radical iodination of the saturated hydrocarbons when they interact with t-BuOI. The activation energy and the rate constants for reaction of hydrogen abstraction by the t-butoxyl radical prove a possibility of the iodination reaction by t-butyl hypoiodite. The probability of participation of polyvalent iodine in the process of iodination is discussed.