A DFT study of radiation induced alkoxy radical formation in crystalline α-l-rhamnose has been performed to better understand the processes leading to selective radical formation in carbohydrates upon exposure to ionizing radiation at low temperatures. The apparent specificity of radiation damage to carbohydrates is of great interest for understanding radiation damage processes in the ribose backbone of the DNA molecule. Alkoxy radicals are formed by deprotonation from hydroxyl groups in oxidized sugar molecules. In α-l-rhamnose only one alkoxy radical is observed experimentally even though there are four possible sites for alkoxy radical formation. In the present work, the origin of this apparently specific action of radiation damage is investigated by computationally examining all four possible deprotonation reactions from oxygen in the oxidized molecule. All calculations are performed in a periodic approach and include estimates of the energy barriers for the deprotonation reactions using the Nudged Elastic Band (NEB) method. One of the four possible radical sites is ruled out due to the lack of a suitable proton acceptor. For the other three possible sites, the reaction paths and energy profiles from primary cationic radicals to stable, neutral alkoxy radicals are compared. It is found that deprotonation from one site (corresponding to the experimentally observed radical) differs from the others in that the reaction path is less energy demanding. Hence, it is suggested that the alkoxy radical formation is not necessarily site specific, but that the observed radical is formed in much greater abundance than the others due to the different energetics of the processes and reaction products.