The adsorption of molecular hydrogen on zeolite X containing various exchangeable cations (Ba, Sr, Ca, Mg) have been simulated employing grand canonical monte carlo (GCMC) procedure for a temperature range of 77-273 K and a pressure range of 0–10 bars. For the hydrogen molecule, the approximation due to Feynman-Hibbs was employed for all the involved dispersion-type interactions in order to account for its quantum nature. The simulation results were compared with experimentally measured values at 77 K and indicated a good quantitative agreement. The results showed that hydrogen adsorption in zeolites is strongly dependent upon temperature, and also on cation type in the zeolite framework, and the highest storage capacity was obtained for CaX.