This paper presents a detailed explanation of a technique for automatically generating a mathematical model for machinery systems. The process starts from a relatively small amount of input data and develops the information required to model a mechanical system with Lagrange’s equation. The technique uses elements of graph theory which were developed for electrical networks. The basic identifications required for mechanical systems are: paths from ground to mass centers, the independent loops of parts, if any, and paths associated with applied force effects. The techniques described in this paper have been used successfully in a generalized computer program, DAMN.