The necessity of airplane structural vibration analysis for purposes of design substantiation is indisputed. This paper presents a mathematical techique that accomplishes this end. The technique, once applied to a given airplane, produces an airplane analog which may be modified to include product improvements or to resolve certain areas of difficulty.The mathematical technique is restricted to airplane self-equilibrating motions in n degrees of freedom using cantilevered component modes and a discrete-particle structural component distribution. Equations of motion are developed using energy principles. Particular importance is placed on the manner of generating these equations since this process determines the vibration analysis effectivity, that is, the inertia and stiffness expressions are specified in certain system generalized coordinates and the resulting eigensystem solutions are obtained using a digital computer. Application of the mathematical technique is illustrated using an example problem.