A rapid pressure swing reactor, which conducts reaction and adsorption/desorption st multaneously and is operated in a periodic pressure variation mode, is investigated through computer simulation and optimisation. A general mathematical model which takes account of the-dynamic variation and spatial distribution of properties within the bed has been formulated and described by a set of partial differential and algebraic equations. Both the successive substitution and simultaneous discretisation approaches have been used for determining cyclic steady state. The method of orthogonal collocation on finite elements is employed for the discretisation of both the spatial and temporal domains. Simulation experience indicates that the simultaneous discretisation approach is much more robust and efficient when compared to the successive substitution approach. The optimisation of the rapid pressure swing reactor is studied via the simultaneous discretisation approach. A significant improvement over the equilibrium yield is shown by the optimisation results for a reversible dissociation reaction.