The interactions of methane with Bronsted acid sites in H-ZSM-5 were investigated both experimentally and theoretically. Diffuse reflectance infrared spectroscopy was used to acquire spectra for methane adsorbed on H-ZSM-5 at room temperature and at 77 K. Upon adsorption, the v1 and v3 vibrational bands of methane shift by -15 and -23 cm-1, respectively, and the vibrational band for OH groups associated with Bronsted acid sites shifts by -93 cm-1. Quantum chemical calculations conducted at the DFT level of theory with a 6-31g**++ basis set show that the observed shifts for methane are attributable to the effects of the electrostatic field created by the atoms of the zeolite. To represent the influence of the zeolite on the adsorbed methane correctly, it is essential to take into account the effects of the Madelung field, as well as the local effects of the acid center. The calculated shift in the vibrational frequency of the bridging OH group lies within the range observed experimentally. However, the quantitative agreement of the calculated and observed shift is not as good as that seen for the bands of CH4.