A three-dimensional model of zeolite structures is described. The calculation of diffusivities as a function of temperature and intracrystalline concentration taking into account sorbate/sorbate interactions is based on the Monte Carlo method. Without a fitting parameter the diffusivities calculated in silicalite give a good approximation of experimental data taken from the literature. In contrast to molecular dynamics methods simulation of multi-component systems accompanied by complex chemical reactions is feasible even for a large number of molecules. This is demonstrated for the Methanol-To-Olefin (MTO) sythesis.