A new inorganic ion exchange composite for removing radioactive cesium from acidic waste streams has been developed. The new material consists of ammonium molybdophosphate, (NH4)3P(Mo3O10)4?3H2O (AMP), synthesized within hollow aluminosilicate microspheres (AMP-C), which are produced as a by-product from coal combustion. The selective cesium exchange capacity of this inorganic composite was evaluated in bench-scale column tests using simulated sodium bearing waste solution as a surrogate for the acidic tank waste currently stored at the Idaho National Laboratory (INL). Total cesium loading on the columns at saturation agreed very well with equilibrium values predicted from isotherm experiments performed previously. A numerical algorithm for solving the governing partial differential equations (PDE) for cesium uptake was developed using the intraparticle mass transfer coefficient obtained from previous batch kinetic experiments. Solutions to the governing equations were generated to obtain the cesium concentration at the column effluent as a function of throughput volume using the same conditions as those used for the actual column experiments. The numerical solutions of the PDE fit the column break through data quite well for all the experimental conditions in the study. The model should therefore provide a reliable prediction of column performance at larger scales.