The theory of electrical lines and filters is based on the concept of a characteristic impedance. Similar concepts are permissible for mechanical systems. It thus becomes possible to derive a generalized theory of vibrating systems that is free from insignificant characteristics of the vibrator. The conclusions are illustrated by computations and by measurements for flat plates. The results are used to develop a theory of the propagation of bending waves in plates and shells on lines similar to the theory of reverberation in room acoustics.