Using a multiple regression procedure, X-ray fluorescence analysis has been applied to a 15-element system associated with ceramic supported automobile emissions catalysts. An equation taking inter-element effects into account was used to relate the concentrations and X-ray intensities of the active elements and contaminants deposited on the ceramic substrate. The major elements present in the substrate were intentionally excluded from the regression. The regression coefficients were determined from a set of 240 calibration standards using a multiple linear least-square regression. Elemental concentrations in the standards ranged from 0.05 to ten weight percent. The ceramic matrix was the same in both the standards and the unknowns to be analyzed and constituted at least 85 percent of the total weight of each sample. The regression coefficients were then used to solve for the contents of the elements in unknown samples. Limits of accuracy were determined by using the set of available standards. The performance of the regression was improved in certain cases by imposing constraints on the regression.