In this paper, a new resolution method for the dynamic simulation of a simulated moving bed is presented. A general rate model for each solute and each column is presented for the case of a linear isotherm. A hybrid resolution is developed, in which an analytical solution is used for the solid stationary phase, while the mobile fluid phase concentrations are obtained by numerical resolution. It is illustrated, through a numerical study, that the resolution method is robust. The method is validated by comparison with previously published experimental results. It is also shown that these numerical simulations are obtained much faster than those based on the physical separation process, allowing the use of this resolution method for on-line applications and process control.