The enthusiasm with which forensic NAA has been received since its first use in a 1951 case has been somewhat premature. It was thought that an identical trace element pattern would be conclusive proof of a common origin for two materials. One method for detecting those trace elements is NAA. In this method, a sample is exposed in a nuclear reactor to a low energy neutron flux. A small number of the nuclei of the various stable isotopes of all the elements presents present will capture such a neutron and become radioactive. Although NAA can easily determine a millionth or a billionth of a gram of a trace element, problems arise in the interpretation of the results of the chemical analysis. In identification of trace elements in hair, textile fibers, paint, and glass, too many other factors interfere with the use of NAA as a reliable identification tool. NAA is very useful, however, in unmasking art forgeries by detecting paints with high degrees of purity, thus excluding them from being very old. It is also useful in toxicology determinations of many poisonous elements and in gunshot residue determinations, including the determination of bullet holes, estimating the firing distance, and indicating the hand which recently fired a handgun. The application of forensic NAA as a probative method requires important statistical background data combined with a realistic consideration of all the possibilities. Six references are included.