The process of ablation is calculated for the stagnation region of a flat disk in a radiation-dominated, massive-blowing environment produced in a ballistic range filled with argon. Flow environments are determined by solving the boundary-layer equations while radiative transfer is calculated through a line-by-line spectral computation. The resulting wall heat-transfer rates are coupled with an existing material's response code to determine surface recession and char thickness. The calculation is performed for six 5-cm-diam models made of carbon-phenolic and carbon-carbon composite launched in the Track-G facility at the Arnold Engineering Development Center. Significant surface recessions are predicted to occur for these models due mostly to radiative heating.