After some introductory remarks which outline the problem and special features of its treatment, Section 3 explains how complex notation and the impedance concept can be applied directly to the analysis of mechanical systems. This leads naturally to the first or “direct” method of constructing an electrical “model” of a mechanical system, where a mechanical force is represented by a voltage and a mechanical velocity by a current; a mechanical impedance, i.e. the ratio of a force to a velocity is then represented by a proportional electrical impedance. In this analogy a mass is represented by an inductance. It is shown that this representation, when established for one particular frequency, is valid for all other frequencies.Section 4 shows that there exists a perfectly consistent, alternative method of constructing such an electrical model in which all these correspondences are replaced by their dual counterparts and which is therefore called the “indirect” or “inverse” analog). A mechanical force is here represented by an electric current and a mechanical velocity by a voltage. Accordingly, a mechanical impedance is then represented by an electrical admittance of proportional magnitude; in particular a mass is represented by a capacitance. This analogy has the advantage that it enables a circuit diagram of the electrical model to be copied from the diagram of the mechanical system, if this is drawn in accordance with certain conventions. The circuit diagram found by this method is the dual of the circuit found by the first method, and as it is a routine procedure to draw the dual of a given network the second analogy may also be useful when utilizing the first type of analogy.The paper supplements the development of this method by showing how levers fall into the general scheme of this geometrical correspondence if they are interpreted as auto-transformers. It also shows how the circuits of both these analogies may be found with advantage by an alternative method, by a “method of successive generalization” of simplified systems—again without the need of establishing the equations of performance of the system. When the circuit of the inverse analogy cannot be drawn in a plane without crossing between its branches certain difficulties arise, the solution of which is d with in a separate paper.In Section 5, combined electrical and mechanical systems are discussed. If the mechanical system is represented by an electrical model, then the electromechanical convertor which links it to the electrical system can usually be replaced by a passive electrical four-terminal network-provided the right type of analogy is chosen for constructing the model; we arrive thus at a purely electrical system. The type of analogy to be chosen is the direct one if the electromechanical convertor utilizes the action of electrostatic forces, and the inverse analogy if the convertor utilizes electromagnetic forces.Two appendices give examples of the application of these methods to the treatment of purely mechanical and of electromechanical systems.