Theoretical models for heating, evaporation, material flow, and stress and strain generation accompanying CO2 laser damage mitigation and surface treatment of fused silica are developed to aid understanding of scaling with process parameters. We find that lateral nonlinear heat transport is an important cooling mechanism, more significant than evaporative cooling. Scaling laws relating experiments with different set of parameters are presented. Transverse conduction, together with the increased thermal conductivity at high temperatures, allows a gentle evaporation regime at low laser intensity in which the rate can be controlled via laser fluence. For higher laser intensity, recoil momentum imparted by rapid evaporation generates pressure, which can lead to transverse flow of the melted material. Only a very thin layer can flow because viscosity increases rapidly with depth. Evaporation and flow are subject to instabilities that can impact surace quality, especially surface flatness, if large areas are processed. Also material flow can heal cracks and improve material quality. Analysis of stress indicates that maximal tensile streses of order 0.1 GPa, comparable to the tensile strength, can be generated.