We have developed a rapid, nondestructive technique using energy-dispersive X-ray fluorescence spectroscopy to determine trace element concentrations in samples of archaeological felsite. The method employs a series of secondary targets that are selected to provide optimal sensitivity to groups of elements with excitation energies just below that of the secondary targets. Intensities of element peaks are ratioed to the Compton scatter peak, which serves as an internal standard. Such procedures compensate for small differences in grain-size, sample density, surface irregularity, variable matrix absorption or composition, as well as minor changes in X-ray flux or other instrumental fluctuations. Comparison of the nondestructive method to conventional analysis on crushed samples generally shows agreement within 20%, and better than 10% for some elements. An application example is presented in which analyses of uncrushed felsite chips from a calcalakaline suite are compared to an alkaline suite. Trace element compositions readily discriminate the two groups of archaeological materials. The technique offers the potential to provide a rapid, nondestructive geochemical method to characterize the composition of archaeological materials, thus providing greater constraints on studies of archaeological sourcing, trade routes, and distribution patterns.