Pressure swing adsorption (PSA) is a very versatile technology for gas separation and purification. The widespread industrial application of PSA has called for an efficient set of simulation, design, and optimization methodologies. In previous work by Jiang and co-workers, we used a Newton-based approach to quickly converge the cyclic steady state and design constraints, and a simultaneous tailored approach with the state-of-art nonlinear optimization strategy to design optimal PSA processes. In this work we extend the simulation and optimization strategies to multiple bed systems. Both unibed and multibed frameworks are adopted to describe bed behaviors. The unibed framework models only one bed over a cycle and uses storage buffers to mimic the bed interactions. The multibed framework simultaneously solves all beds but only for a portion of the cycle. Challenges and implementation details of both frameworks are discussed. A five-bed, 11-step hydrocarbon separation process, which separates H-2 from a mixture of H-2, N-2, CO2, CO, and CH4, is used for illustration. By manipulating valve constants, step times, flow rates, and bed geometry, the optimizer successfully maximizes H-2 recovery, while meeting product purity and pressure specifications. (C) 2004 American Institute of Chemical Engineers.