Ammonium molybdophosphate (AMP) immobilized on polyacrylonitrile (PAN) is an engineered form of cesium selective sorbent material developed at the Czech Technical University in Prague. A form of a second order kinetic model is applied to experimental AMP–PAN breakthrough data. A system utilizing three fixed beds in series is described that allows for continuous nuclear waste processing at approximately 890 l/h. This process would yield a product stream that is below the NRC Class A low level waste limit for 137Cs, and would result in high activity waste volume reduction factors of approximately 2200 and 570 for liquid sodium bearing waste and dissolved calcine waste, respectively, which are currently stored at the Idaho National Engineering and Environmental Laboratory.