The dynamic behavior of a multistage agitated contactor has been numerically studied for its potential use for catalytic hydrogenation of nitrile butadiene rubber. A model consisting of stirred tanks in series with back flow is applied to describe the flow behavior in the presence of hydrogenation within a multistage agitated contactor of six stages. The coupled behavior between kinetics and mass transfer is analyzed by manipulating parameters involved in the model. The model predicted that the performance of the reactor is completely governed by the ability of the catalyst in activating hydrogen, the loading level of C=C double bonds, the relative capacity of the reaction to mass transfer, and the backmixing. Mass transfer and backmixing are important factors for the hydrogenation process and enhancing mass transfer and minimizing backmixing helps in increasing hydrogenation conversion. The effects of backmixing and the number of stages for the hydrogenation are discussed, and optimal operation conditions are suggested.