The DFT calculations were applied to investigate the impact of the nature of bivalent cations M (M = Mg2+, Ca2+, Sr2+, Zn2+, Mn2+, Co2+, Ni2+) in cation-exchanged ZSM-5 zeolites on the Lewis acid site (LAS) strength. Intensities and shifts of IR stretching bands of adsorbed methane were calculated. Adsorption leads to a decrease in their frequencies and a marked increase in the intensities of the symmetric stretching band of methane. At the same time the intensities of the asymmetric stretching bands decrease. To characterize the strength of LAS, Fukui functions were computed. A good linear correlation between the intensity of methane vibrations and the LAS strengths (Fukui function f(+)) was found.