For the first time, the monovalent cation positions in a zeolite, i.e., mordenite, with increasing SI/Al ratios are calculated from combination of Monte Carlo techniques and Si-29 NMR spectroscopy. For each Si/Al ratio, a combination of solid-state Si-29 NMR and Monte Carlo simulations is used and leads to the proposal of a realistic structural model where the aluminum atoms are distributed among the four possible crystallographic sites. Then, the positions of the cations stabilizing the mordenite lattice are obtained by using Monte Carlo simulated annealing. The populations of the sites occupied by the cations and their variations with the Si/Al ratio predicted by the model are in very good agreement with those measured by thermally stimulated current spectroscopy on Na-mordenites.