Ten samples of the Martian regolith have been analyzed by the Viking lander X ray fluorescence spectrometers. Because of high-stability electronics, mechanism inclusion of calibration targets, and special data encoding within the instruments the quality of the analyses performed on Mars is closely equivalent to that attainable with the same instruments operated in the laboratory. Determination of absolute elemental concentrations requires gain drift adjustments, subtraction of background components, and use of a mathematical response model with adjustable parameters set by prelaunch measurements on selected rock standards. Bulk fines at both Viking landing sites are similar in composition, implying that a chemically and mineralogically homogeneous regolith covers much of the surface of the planet. Important differences between samples include a higher sulfur content in what appear to be duricrust fragments than in fines and a lower iron content in fines taken from beneath large rocks than those taken from unprotected surface material. Further extensive reduction of these data will allow more precise and more accurate analytical numbers to be determined and thus a more comprehensive understanding of elemental trends between samples.