Thermal Neutron Activation Analysis with Instrumental Ge(Li) Gamma Spectrometry was used to determine the amounts of more than 30 trace constituents in heart tissue of rats and kidney tissue of rabbits. The results were confirmed by a rapid ion-exchange group separation method in the initial stages of the experiments. The samples were exposed to thermal neutrons for periods between 3 minutes and 14 hours. Significant differences in the amounts and types of trace elements in the two different tissue types are apparent, however, are probably due to specific diets. Tables of relevant nuclear data, standard concentrations, radiochemical separation recoveries, and quantitative analytical results are presented. The ion-exchange group separation scheme and typical examples of the instrumental gamma ray spectra are shown. The techniques developed in this study are being used for a large scale constituent survey of various diseased and healthy human tissues.