This work presents the detailed mathematical modelling and advanced optimization of a number of zeolite membrane process structures for gas separations. First, a general model for the separation of binary gas mixtures is developed based on the generalized Maxwell-Stefan (GMS) approach. Accordingly, the model is used in the simulation of various process structures including co-current and counter-current operation, recycle modules and membrane cascades. The model is validated against available experimental data of methane-ethane and methane-propane mixtures on silicalite membranes. A non-linear programming approach is then employed to determine optimal design options for different process performance objectives. Various trade-offs between different optimization objectives are systematically revealed. The impact of the detailed GMS model on the optimization results is investigated through a comparison with corresponding results obtained using the single-file diffusion model, which ignores diffusional adsorbate-adsorbate interactions.