We report a computational study on how alkali and alkaline earth metal cations affect the Bronsted acidity of a bridging OH group in their close vicinity. The zeolite fragment is modeled as a six-ring of faujasite structure which contains two or three aluminum centers. The calculations show that charge compensation by alkali or alkaline earth metal cations decreases the deprotonation energy (DE) of the bridging OH group relative to the completely protonic forms of the clusters; i.e., mixed forms of zeolites which contain both protons and metal cations for charge compensation exhibit sites that are more acidic than the corresponding pure protonic forms. The strongest decrease in DE is found for calcium and sodium exchanged model clusters. An analysis of the properties of the bridging OH groups and the trends in calculated DE values reveals that the contribution of the metal cation to the stabilization of the deprotonated form of the cluster is important for the reduction of DE of the considered bridging OH group. We also discuss the influence of the metal cations on the core level shifts of the zeolite oxygen centers.