Internal swelling reactions (ISR) can affect long term duration of reinforced concrete (RC) structures by causing cracking and expansion of concrete material. These pathologies mainly consist in Alkali Aggregate Reaction (AAR) and/or Delayed Ettringite Formation (DEF). Thus, it is necessary to provide robust predictive numerical models able to re-assess the mechanical state of affected structures. A new numerical strategy is proposed in this paper to compute the evolution of the ISR reaction from intrinsic parameters to be identified for the reactive concrete. Based on Larive's model, evolution of the chemical strain is written in order to assume the irreversibility of the mechanisms and to take into account time history of the Relative Humidity and Temperature supported by the concrete specimen. An effective time is proposed to store history of the reactive concrete and to be able to compute evolution of the chemical strain.