A mathematical model of a simulated countercurrent moving bed chromatographic reactor (SCMCR) has been developed. The model represents a multiple column reactor consisting of a series of either four or five tubular fixed beds packed with a mixture of catalyst and adsorbent, with a port that can serve either as an inlet or an outlet between each. A reversible first order reaction, A reversible arrow B, with rate coefficients and rate parameters taken from the hydrogenation of 1,3,5-trimethylbenzene is incorporated into the model. The partial differential equations governing the isothermal reactor at 463 K are solved by an adaptive finite element method with uneven grid points. Model predictions of concentration profiles in the columns, and overall reactor performance, are obtained. It is shown that reaction and separation occur simultaneously, and that the conversion of this equilibrium limited reaction is greatly increased over the 0.62 that would be the maximum obtainable in a non-separative system. Under appropriate operating conditions, the model calculations predict that high product purity streams (98-99%) and nearly unit conversions can be obtained.