Two procedures are described for fitting spectrometric analytical functions with a digital computer and conversion of instrument readings to element concentrations. The first procedure is intended for computers giving rapid response, and particularly those which can operate in the conversational mode. During the running of the program, the user decides on the equation to be used and whether data for any standards are to be rejected. The second procedure is intended for use on batch-loading computers; these decisions are incorporated in the program. Results are given of the use of both procedures. The occasional failures of the procedures are discussed, and methods are described for detecting such failures. A discussion is given of a method for including an estimate of the uncertainty of the analytical function in the estimated analytical error. © 1969, American Chemical Society. All rights reserved.