An elastic panel is excited by a time harmonic force and the power flow is calculated, averaged over a frequency band and all source positions. The two-dimensional problem is investigated asymptotically, for frequencies that are sufficiently high to ensure that many panel modes are near resonance. The asymptotic results are different according as the frequency is above or below the coincidence value; in the latter case account has to be taken of both resonance and non-resonance contributions to the power flow. A transition formula is given for frequencies near coincidence and the results agree well with numerical calculations. Corresponding results are given for the three-dimensional problem of the rectangular panel and previous theory is justified and extended.