A Rutherford backscattering spectrometry facility has been designed and built at the University of Arizona. Initial calibration and testing has been carried out in order to accurately characterize the system and make it ready to perform reliable analyses. Also, an explanation of basic RBS principles has been presented to enable persons unacquainted with the technique to determine its applicability for various types of analytical problems. A method for determining the concentration profile of Ag in an SiO₂ matrix is carefully explained. Calculations derived from basic principles are demonstrated for this analysis and can be applied in a number of similar circumstances. Several other examples of analyses of utilizing various operating parameters are explained and illustrated. Some examples of unusual samples are shown to be feasible for analysis by this technique. RBS is shown to be a very useful analytical tool for a wide variety of samples. It has the capability of performing quantitative depth profiles without standards. The vast potential for its use by analytical chemists is demonstrated, and future improvements for this particular facility are discussed.