The mathematical basis for a computer code PUSEP (Plutonium Uranium Solvent Extraction Program) for the analysis of partitioning cycle of PUREX process involving in-situ electrochemical reduction of uranium and plutonium is described in the present investigation. The basis of development of model equations involves countercurrent multi-component extraction coupled with chemical and electrochemical reactions. The model is specific to mixer-settler contactors and is restricted to mass transfer equilibrium. The components considered in the model equations are U(VI), U(IV), Pu(IV), Pu(III), nitric acid and hydrazine. Computer code provides transient behaviour of mixer-settler contactor from the start-up conditions to the steady-state conditions. The code has been validated with the experimental data available in literature. The calculated results are consistent with the experimental results considering the major components mentioned above.