The mathematical basis for a computer code PUNE (Plutonium-Uranium-Non-Equilibrium) is described. The code simulates the steady-state concentration profiles of solvent extraction contactors used in the Purex process under conditions where material transfer between phases deviates from the equilibrium limit. The deviation is accounted for by a mass transfer area characteristic of the operating conditions of a contactor, and a mass transfer coefficient for the chemical species of interest. In the limit of infinite mass transfer rate, PUNE gives the same results as other codes that calculate equilibrium profiles. For 1A and IE contactors, the computational times are reduced between two- and fivefold over times required by other codes that generate the steady-state profiles via transient state conditions. For 1B or partitioning contactors, the reduction in time can be more than 20-fold. Since there is no loss of accuracy in these calculations, PUNE represents an important advance in the determination of steady-state profiles, especially for 1B contactors because it is with these that the greatest computational difficulties are encountered.