The buildup of xenon poisoning is a prime factor in restarting a high-flux thermal reactor after shutdown. To restart the reactor at any time, sufficient excess reactivity must be present to override the xenon poisoning. The amount of excess reactivity required can be minimized by determining an optimum reactor shutdown program. Based on Pontryagins Maximum Principle, optimum shutdown programs are determined for various flux levels ranging from 1014n/cm2 sec. to 1016n/cm2sec. Results show that a considerable reduction in the peak value of xenon concentration can be realized by relatively simple shutdown programs.