An analytical solution for linear ideal simulated moving bed (SMB) chromatography is derived. This solution is a set of algebraic equations which allows the calculation of the concentration profiles along the columns and of the concentration histories at the raffinate and extract ports. Using this solution, the operations of SMB under steady-state conditions and during the transition from start-up to steady state are examined. An asymptotic property is found for the steady state. A comparison between SMB and true moving bed (TMB) illustrates their similarities and differences.