The application of computer graphics (CG) and molecular dynamics (MD) to the investigation of structures and functions of heterogeneous catalysts was demonstrated to display the deposition and sintering of ultrafine metal particles on matal oxide support. The Au atoms in the Au cluster moved considerably with time even at 300K, and the movement of atoms became more evident with rise in temperature. In agreement with the mobility of Au cluster and MgO (100) plane, the shape of Au cluster changed significantly during the deposition process of Au cluster on MgO (100) plane, while the position of Mg and O ions at MgO (100) plane did not change appreciably. The shape of Au cluster after the deposition also changed markedly by the interaction potentials between Au and MgO. The sintering process of two Au clusters attached on MgO (100) plane was satisfactorily simulated, suggesting that the MD and CG are useful for investigating the deactivation mechanism of supported metal catalysts which are important in relation to the automotive exhaust gas control. The MD and CG methods were also applied to the molecular sieving effect of A-type zeolites in the diffusion and separation of O2 and N2. For CaNaA zeolite having the open 8-membered ring window, both N2 and O2 molecules moved freely through the window. For NaA zeolite having Na+ ions at the window, the diffusion behavior changed greatly, affected by the kind of molecule structure and temperature. At higher temperatures, both N2 and O2 are caused to migrate through the window. At lower temperatures, the separation of O2 and N2 was simulated and dynamically visualized. The mobility of Na+ cation at the window was found to be the cause for the significant difference in the molecular sieving effect of NaA, at different temperatures. MD and CG were applied to investigate the role of zeolite framework in the direct decomposition of NO to N2 and O2 on Cu-ZSM-5 catalysts. On the basis of the calculated results for various states of Cu+ and Cu2+ ions in ZSM-5, the relative stability of Cu+ to Cu2+ in ZSM-5 was found to provide one of the reasons for the high activity of Cu-ZSM-5. By calculation, increase in Si/Al ratio in Cu-ZSM-5 would be favorable for the reaction, which is in agreement with experiments.