This research had several objectives. One was to review the literature to determine methods of trace element preconcentration that could be used realistically for sample preparation for trace element determinations in drinking, natural and/or effluent waters. Elements included in the USEPA's listing of Priority Pollutants, with the exception of beryllium, were chosen for the study. Once the methods were identified, those deemed most promising for application to the simultaneous determination of trace elements using energy-dispersive x-ray fluorescence (EDXRF) spectrometry were to be evaluated. Several criteria were used such as the number of elements recovered, linear dynamic range, accuracy and precision, sensitivity-recovery, resistance to interferences and overall ruggedness of the method. Seven methods were eventually selected for detailed evaluation. Systematic experiments were conducted using bilevel factorial experimental designs for interference studies and single element evaluations of response parameters. The interference studies assessed interferences by concomitant elements, sodium chloride, calcium chloride, and humic organic materials. These choices were made to emulate, as closely as possible, conditions expected to be encountered in natural samples. A numerical rating scheme was devised for the procedures and these values were used to select two optimum methods.