In this work, we report grand canonical Monte Carlo (GCMC) simulations of adsorption of polar and nonpolar molecules such as xenon, methane, and p- and m-xylene in the NaY zeolite at different temperatures. The adsorption isotherms as well as the curves giving the evolution of the isosteric heat with coverage have been calculated and compared to their experimental counter;parts and to other simulation results when available. This work is based on a new adsorbate-zeolite potential function. In the particular case of adsorption of xylene isomers, we also report a detailed structural analysis of the sorbed phases.