Cesium-137 is a common radioactive byproduct found in nuclear spent fuel. Given its 30 year half life, its interactions with potential storage materials-such as cement paste-is of crucial importance. In this paper, simulations are used to establish the interaction of calcium silicate hydrates (C-S-H)-the mam binding phase of cement paste-with Cs at the nano- and mesoscale. Different C-S-H compositions are explored, including a range of Ca/Si ratios from 1.0 to 2.0. These calculations are based on a set of 150 atomistic models, which qualitatively and quantitatively reproduce a number of experimentally measured features of C-S-H-within limits intrinsic to the approximations imposed by classical molecular dynamics and the steps followed when building the models. A procedure where hydrated Ca2+ ions are swapped for Cs1+ ions shows that Cs adsorption in the C-S-H interlayer is preferred to Cs adsorption at the nanopore surface when Cs concentrations are lower than 0.19 Mol/kg. Interlayer sorption decreases as the Ca/Si ratio increases. The activation relaxation technique nouveau is used to access timescales out of the reach of traditional molecular dynamics (MD). It indicates that characteristic diffusion time for Cs1+ in the C-S-H interlayer is on the order of a few hours. Cs uptake in the interlayer has little impact on the elastic response of C-S-H. It leads to swelling of the C-S-H grams, but mesoscale calculations that access length scales out of the range of MD indicate that this leads to practically negligible expansive pressures for Cs concentrations relevant to nuclear waste repositories.