The mathematical basis for a computer code PUMA (Plutonium-Uranium-Matrix-Algorithm) is described. The code simulates steady-state concentration profiles of solvent extraction contactors used in the Purex process, directly without first generating the transient behavior. The computational times are reduced, with no loss of accuracy, by about tenfold over those required by codes that generate the steady-state profiles via transient state conditions. Previously developed codes that simulate the steady-state conditions directly are not applicable to partitioning contactors, whereas PUMA is applicable to all contactors in the Purex process. Since most difficulties are encountered with partitioning contactors when simulating steady-state profiles via transient state conditions, it is with these contactors that the greatest saving in computer times is achieved.