As part of an ongoing development, this paper presents a brief description of a new Chemo-Mechanical (C-M) model for the expansions due to Alkali-Silica Reaction (ASR) in concrete. This model has been formulated at the meso-scale level (major aggregate fraction and cementitious matrix of cement paste or mortar). The chemical and the mechanical problems are solved by means of two different Finite Element (FE) codes coupled via a staggered implementation. Both codes use the same FE mesh, which can include zero-thickness interface elements in between continuum elements in order to simulate localized cracks. The chemical model consists of the three main diffusion/reaction field equations for the concentrations of aqueous Alkali, Calcium and Silicate ions in the pore solution, complemented by a number of chemical kinetics and chemical equilibrium equations. The volume fraction distribution of the solid constituents of the hardened cement paste, the aggregates and the reaction products (ASR gel) evolve with the progress of the reaction. Diffusion-reaction process can occur in both continuum and interface elements. The meso-mechanical model for concrete has the distinctive feature of considering lines in the FE mesh as potential crack lines, via the systematic use of zero-thickness interface elements, equipped with traction-separation constitutive models based on principles of non-linear fracture mechanics, while the matrix phase is considered elastic or linear viscoelastic. The proposed coupled model has been applied to some simple verification examples. The results show the good performance of the model and the individual physical consistency and reasonable interaction among the variety of ingredients (mechanical, chemical, etc.) involved.