Surface patterns have been shown to occur on slender re-entry vehicles that use ablative materials as a thermal protection system. One pattern of interest is a regular pattern called cross-hatching. The mechanism which causes cross-hatching is not yet well understood. A series of experiments at the von Karman Institute were conducted in the 1970s to attempt to quantify the characteristics of the ablation patterns but no computation with modern numerical methods has been used to simulate this phenomenon. In this paper, stability analysis is conducted for these flow field conditions and an ablation boundary condition is implemented and validated to aid in future numerical simulations of these patterns.