The flexural vibration of an infinite elastic beam which is excited by a localized harmonic driving force and attached over its entire length to a thin elastic plate of infinite extent is investigated theoretically. The results are expressed in terms of two parameters,kbLandr. The parameterkbLdescribes the frequency dependence and degree of beam‐plate coupling; and the parameterris the ratio of flexural wave velocity on the plate to that on the beam. Forr1, plate excitation is localized near the beam. In geometries of practical interest, the strong radiation case prevails. Small deviations in the input admittance of the beam from that of a free beam are initially obtained by employing a perturbation procedure which is valid in the limitkbL≫1, the relevant range for geometries of practical concern. In addition, a variational principle for the admittance is constructed and shown to yield the results of the first‐order perturbation solution when the displacement of a similarly excited free beam is used as a trial function. At very high frequencies the input admittance is found to approach that of a free beam, while at lower frequencies it is found that the plate adds an additional stiffness susceptance to the input admittance. For a typical beam‐plate geometry it is found that the beam is affected by the plate for all forcing frequencies below about 5000 cps and may be estimated by the results of the present calculation down to a few hundred cps.