A combination of quantum chemistry (QC), molecular dynamics (MD), and computer graphics (CG) methods was applied for investigation of the adsorption and the mechanism of methane activation on Ga3+-exchanged ZSM-5 catalyst. Quantum chemical density functional calculations were performed for the system of a MD-derived model cluster of zeolite and methane or water molecules. In the initial step the methane molecule was found to undergo weak physical adsorption on a Ga site at a distance between gallium and carbon atoms of 2.9 Angstrom and an adsorption energy of -4.90 kcal/mol. In the next step the dissociative adsorption of methane was studied. The dissociated complex with CH3 attached to Ga at 2.0 Angstrom and H bonded to extraframework oxygen appeared to be very favorable and led to energetic stabilization of -63.0 kcal/mol. On the contrary, no stable physisorbed state of water was observed, but the dissociated form of H2O appeared to be strongly bonded at the Ga site. The comparison of both processes allows for the discussion of the influence of water poisoning on the activation process. The adsorption energy of the dissociated water molecule at the optimized geometry is -77.5 kcal/mol, substantially larger than that of a physisorbed or dissociated methane molecule. This may result in prevention of methane activation, because methane adsorption on a Ga site already poisoned by water seems too weak to allow for any further transformation.