Simulated moving bed (SMB) chromatography is a well-established technology for separating chemical compounds. To describe an SMB process, a finite-dimensional multistage model arising from the discretization of partial differential equations is typically employed. However, its relatively high dimension poses severe computational challenges to various model-based analysis. To overcome this challenge, two Krylov-type model order reduction (MOR) methods are proposed to accelerate the computation of the cyclic steady states (CSSs) of SMB processes with linear isotherms. A "straightforward method" that carefully deals with the switching behavior in MOR is first proposed. Its improvement, a "subspace-exploiting method," thoroughly exploits each reduced model to achieve further acceleration. Simulation studies show that both methods achieve high accuracy and significant speedups. The subspace-exploiting method turns out to be computationally much more efficient. Two challenging analyses of SMB processes, namely uncertainty quantification and CSS optimization, further demonstrate the accuracy, efficiency, and applicability of the proposed methods. (C) 2014 American Institute of Chemical Engineers