This study concerns the transmission of vibrational energy through beam-plate junctions by energy flow analysis, which is an analytic tool for predicting the frequency averaged vibration response of built-up structures in the medium to high frequency ranges. A semi-infinite beam perpendicularly connected to an infinite plate is studied using the wave transmission approach. To calculate the power transmission and the reflection coefficients of the beam-plate junction, compatibility and equilibrium conditions are applied when each wave component is incident on the beam and plate, respectively. Power coefficients are calculated and plotted against frequencies for different dimensions and the directivity pattern of the scattered waves in the plate show close agreement with that of the rigid inclusion as the frequency increases. The results obtained are applied to the finite beam and the circular plate coupled structure, and the energy densities obtained from energy flow analysis show better agreement with analytic solution results as frequencies are increased.