The safety analysis for the Advanced Neutron Source Reactor (ANSR) required the development of a new analysis technique to determine fuel integrity and to assure avoidance of critical heat flux (CHF) conditions. The ANSR is a research reactor design intended to provide the highest continuous neutron beam intensity of any reactor in the world. Reliance on previous safety analysis techniques such as those used in the High Flux Isotope Reactor would result in a design that would not meet the requirements. A more accurate but still conservative analysis technique was developed for the ANSR safety analyses. This technique, the local analysis technique (LAT), relaxed some of the overly conservative assumptions of previous hot-spot studies by using a large number of detailed analyses. The conditions used in these analyses were spread over the possible distributions found in specific designs. This technique was used to analyze several core designs to produce confidence in the fuel plate integrity that could be damaged by excessive fuel temperatures and avoidance of CHF conditions. This approach can be used for other reactor designs and should allow increases in the operating power levels. Alternatively, the LAT could be used to demonstrate increased safety margins for present operating conditions.