In this paper, we present a novel finite element model to simulate alkali-silica reaction in a realistic concrete meso-structure. Application of the internal ASR loading leads to the evolution of multiple deviated cracks and corresponding macroscopic expansion. A particular crack-extension algorithm and a solution scheme provide numerical stability and allow to model complicated crack patterns while preserving the physics. The predictive validity of the model is demonstrated by matching an analytical solution of a loaded penny-shaped crack. The model is applied to the experimental dataset comprising the time-evolving X-ray tomograms of the ASR-affected concrete. Similar to the tomography data, the model results in an expanded concrete sample with a developed crack network. Two hypotheses on the crack loading and extension mechanisms are tested by comparing the crack statistics. Simulations with varying number of ASR sites and application of the uniaxial loading bring interesting insights. The latter concerns the role of the ASR-sites number, the individual loading amplitude and the difference in crack patterns.