Modeling the behavior of alkali aggregate reaction (AAR)damaged concrete is made complex by the large number of elementary physical phenomena to be taken into account (concrete reactivity, thermal activation, moisture dependence, concrete rheology, and damage interaction). This paper presents the elementary physical principles that lead to the formulation of a visco-elasto-plastic orthotropic damage model including chemical pressure induced by AAR. Particular attention is also paid to the modeling of moisture effects on AAR development and on drying shrinkage. The constitutive modeling proposed is developed into the framework of an anisotropic damage theory to realistically model the strong cracking anisotropy and swelling observed on affected reinforced beams. This paper is followed by a second one in which a calibration procedure is given for the model parameters and experimental results are used to verify the capability of the model to describe the mechanical behavior of degraded structures under various environmental and loading conditions.