Moisture transfers have a major effect on concrete durability. For Alkali-Silica Reaction (ASR), chemical swellings depend on water content, and drying can have important consequences. Within the framework of a large experimental study developed in partnership by the Laboratoire Central des Ponts et Chausses (LCPC) and Electricit de France (EDF), the continuous measurements of moisture transfer in reactive concrete structures was one of the main purposes. This paper deals with the large data bank on concrete drying and water absorption, measured on six 3 in long beams with weighing and gammadensitometry devices specially designed for this study. These measurements enable some quantitative conclusions to be reached. Moreover, the data allows the validation of models of moisture transfer representing the mass variation with time in the beams. Profiles of mass variations thus obtained are the mandatory first step of calculations to estimate the mechanical behaviour of these reference or ASR damaged beams.