To suppress cracking during cool down, a numerical simulation of the growth system was used to understand the correlation between the furnace power during cool down and the radial temperature differences within the crystal. The critical radial temperature difference, above which the crystal cracks, has been determined by benchmarking the simulation results against experimental observations. Based on this comparison, an optimal three-stage ramp-down profile was implemented and produced high quality, crack-free Yb:S-FAP crystals.