Molecular dynamics simulations have been performed to study the diffusion of-a mixture of benzene and propylene, for the cumene synthesis process, in purely siliceous MWW (MCM-22), a zeolite containing two separate channel systems: the 10-member ring (MR) sinusoidal and the 12-MR supercages interconnected by 10-MR windows system. The diffusion processes in each channel system of MWW at 650 K have been studied independently. We have found that in order to obtain quantitative or semiquantitative diffusion coefficients, the framework should be optimized. A large diffusivity for propylene in both channel systems, and especially in the supercage system, is observed, whereas benzene is not seen to diffuse in either of the two channel systems, and only intracage mobility is seen in the supercage voids. The positions of minimum energy, where the molecules are expected to react, have been located in both channels. The diffusion of benzene in the supercage system seems to be temperature-activated, and when the temperature is increased, intercage diffusion will probably occur. Radial distribution functions show that condensation reactions between benzene-propylene and propylene-propylene are possible, which indicate the necessity of working in an excess of benzene. The results of the simulations of diffusion suggest that the formation of cumene probably occurs at the external surface or close to the external surface of the MCM-22 zeolite crystals.