Abstract Linear vibration of a coupled string–rigid bar system is investigated. Owing to dynamic interaction between the strings and the rigid bar, the coupled system is not self-adjoint in its original equations of motion. Consequently, the classical modal analysis cannot be applied. This study develops an augmented formulation for the eigenvalue and boundary value problems of the coupled system. In this formulation, orthogonal eigenfunctions are obtained, and the general response of the coupled string–bar system is represented by an eigenfunction series. Green’s function formula for the coupled system is derived by two methods: modal analysis and Laplace transform. The analytical predictions about the system eigensolutions and response are illustrated in numerical simulation.