X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) have long been used for sputter depth profiling for the determination of sample chemical composition as a function of depth. Often in XPS and AES, peak overlap or a subtle change in chemistry makes the chemical analysis of the elements in a material difficult. By using a variety of numerical methods, such as linear least squares fitting and target factor analysis, it is possible to improve the analysis and interpretation of depth profiles. The use of numerical methods can aid in the interpretation of chemical state information and in most cases significantly improves the detection limits of specific elements. An XPS sputter depth profile of tantalum silicide on silicon and an AES profile of a multilayer structure of gold, tantalum, and silicon carbide are shown as examples of the improvements offered by applying numerical methods.