Summary: It has been proposed that the flow of mechanical energy through a structural/acoustic system may be modeled in a manner similar to that of flow of thermal energy in a heat conduction problem. If this hypothesis is true, it would result in relatively efficient numerical models of structure-borne energy in large built-up structures. Fewer parameters, are required to approximate the energy solution than are required to model the characteristic wave behavior of structural vibration by using traditional displacement formulations. The energy flow hypothesis is tested in this investigation for both longitudinal vibration in rods and transverse flexural vibrations of beams. The rod is shown to behave approximately according to the thermal energy flow analogy. However, the beam solutions behave significantly differently than predicted by the thermal analogy unless locally space averaged, energy and power are considered. Several techniques for coupling dissimilar rods and beams are also discussed. Illustrations of the solution accuracy of the methods are included.