In predicting the effectiveness of quieting measures for reducing machine-induced structural vibration, it is necessary to know the vibratory output of the machine and the dynamical properties of both the machine and the supporting structure. In many vibration reduction problems, even if the causes of the vibratory output of the machine are known (e.g., unbalance, combustion processes, friction, fluid flow), the magnitudes of the excitations, their points of application, and the transfer functions thence to the machine output terminals (the mounting points) are unknown; hence, prediction of vibratory output is difficult. It follows that a method for predicting structural vibration, and the effectiveness of quieting measures, which would utilize data available at the output terminals of the machine, and input terminals of the supporting structure would be of considerable utility. This paper proposes such a method, which makes use of multi-terminal multi-degree-of-freedom mechanical generalizations of the Thevenin and Norton electrical network theorems. The quantities for characterizing the vibratory output of the machine, its dynamical characteristics, and the the dynamical characteristics of the supporting structure are defined, and problems in obtaining the required experimental data are briefly discussed.