This article investigates the power flow of the three-beam system on Winkler–Pasternak elastic foundations under elastic boundary conditions. The time-averaged power flow of the beam on elastic foundations with elastic boundary conditions is calculated based on the internal shear force and bending moment and the wave propagation approach. The reliability and accuracy of the calculation method are verified by comparing the vibration acceleration calculated by calculation examples and the finite element method. In addition, the effects of structural parameters and boundary conditions on the power flow of the three-beam system are investigated. This contributes to the analysis of the dynamic characteristics of the beam on double parameter elastic foundations under complex boundary conditions.