The steady-state structure of a tokamak scrape-off plasma within a divertor chamber is numerically modeled. The simulation code OAKLEAF approximates the relevant atomic and molecular hydrogenic physics within the plasma as well as examining the effects of several wall impact events including charged particle reflection, absorption, and re-emission, secondary electron emission, and the sputtering of wall material by incident particles. Results indicate the presence of a two parameter solution space. With appropriate choices for these parameters the simulation code produces the electrostatic potential and density profiles within the divertor system as well as snapshots of the particle distribution functions at several points in the chamber. Using the distribution function information the model determines the detailed particle fluxes incident to the divertor plate and calculates the resulting sputtering rates. A study of sputtering rates as a function of initial plasma temperature is then presented. The work concludes by reviewing the scope of the thesis and by making recommendations for future work in the area.