The mathematical basis for a new computer code, CUSEP-MOD1, is described. This new code allows the calculation of the temporal response of pulsed column contactors with sieve plates in which spent nuclear fuel is reprocessed using the Purex process. The CPU times needed for these calculations are shorter than those using the CUSEP code but longer than those using the PULSER code, these latter codes having been described previously. Although PULSER remains the faster code, it utilizes approximations that would make CUSEP-MOD1 the preferable code for many applications. The improved efficiency of CUSEP-MOD1 is based on an analysis of the correlation of the aqueous and organic flows in pulsed columns. The analysis shows that both phases move with positive correlation at zero lag time because of the magnitude of the impressed pulsed flow. The new code gives concentration profiles virtually identical to those of the CUSEP code and replaces CUSEP for calculation of the temporal and steady-state concentration profiles in pulsed column contactors. A comparison is made of the steady-state concentration profiles in an exemplary extraction (A-type) contactor calculated using CUSEP, CUSEP-MOD1, and PULSER.