Describes a new method for analyzing linear systems, called the generalized number method, and its application to the analysis of electrical circuits with time-independent concentrated parameters and weak signals. The method is based on mapping the properties of a given linear system by sets of digital indices and a strict sequence of operations on these sets. The advantage of this method is to reduce the amount of calculations when analyzing complex circuits and to simplify the programming of the digital computer to obtain results not only in the form of numbers, but also in the form of analytical (letter) expressions of the desired circuit functions.