The main goal of this work is to introduce two numerical techniques used to simulate the soot combustion in plumes, and examine the impact of the flow and plume characteristics on the soot combustion process. This work represents our first step toward an accurate prediction of soot oxidation, its effect on the radiation pattern, and the maximum radiation in underexpanded plumes. As the soot concentration in plumes is very low and does not affect the fluid dynamics or chemical kinetics mechanisms of the plume flow, an overlay approach is chosen to separate the computation of the plume flow from that of the soot. Both kinetic and continuum approaches for the soot overlay problem are presented for the example problem of a single-nozzle axisymmetric plume representative of the Atlas rocket. Results are presented to demonstrate the sensitivity of soot oxidation to the initial spatial distribution of soot at the nozzle exit plane, changes in oxygen density and temperature levels, and changes in soot particle size.