The theoretical model of Sherman and of Shiraiwa and Fujino for monochromatic excitation has been made the basis for a widely applicable, quantitative, and fast X-ray fluorescence method. Excitation was achieved with radioisotopic X-ray sources while detection was energy-dispersive, assuring that no important component was being neglected. Published values of mass attenuation coefficients, quantum yields, etc., were used in a rapidly converging, iterative calculation, which finds the elemental concentrations consistent with the observed fluorescence intensities. Weight fractions of elements not being determined are entered as known values. One element or compound may be used for normalizing. The wide application of the method is illustrated by the fact that the same aqueous standards may be used for the analysis of either steels or silica-based catalysts. No additional calibrations are needed to take care of enhancement effects since the model is explicit and contains only fundamental constants in the enhancement term. Samples which are smaller than the effective X-ray beam may also be analyzed if a normalizing element is not used. The computer program assumes an infinitely thick sample; however, an option is provided for thinner samples if the weight and area are provided. The calculation has been programmed on a programmable desk calculator as well as a large time-sharing computer and a dedicated mini-computer. The latter allow the storage of the full table of attenuation coefficients, from which the constants of interest can be read as desired.