The alkali-silica reaction (ASR) is a chemical reaction that causes expansions and unexpected deformations of concrete structures. A methodology of assessment of ASR-damaged structures is required in order to evaluate their structural stability. Chemomechanical calculations have been performed in order to investigate the assumption of modeling ASR-induced expansions as imposed strains. The input data for the model comprises the moisture distribution in the damaged structures, ASR-induced potential strains, and the influence of ASR on the concrete mechanical properties. The results of calculations have been compared with experimental data obtained from ASR-damaged beam specimens. The role of water supply and reinforcement has been analyzed in comparing the deformations of plain and reinforced concrete beams subjected to a moisture gradient. Calculations show that cracking and compressive stresses (here induced by steel reinforcement) have a large influence on the anisotropy of the ASR swellings. This induced anisotropy is shown to be one of the main factors that should be considered while predicting the mechanical behavior of ASR-damaged structures.