The response of beams and plates to fluctuating loads with high mean values is considered. The static deformation is obtained separately; the vibration of the statically deformed structure is then discussed in terms of the induced static in‐plane membrane stresses. It is shown that the response of a deformed plate can be predicted by defining an effective uniform tension. Simple expressions are obtained for the loss factor in terms of the impedance of the supports of the beam or plate. Expressions are given for the changes of modal resonance frequencies and loss factors due to the tension, with the assumption of constant boundary impedance. The predicted changes in loss factors agree quite well with some previously published experimental data for very thin plates. The changes for most cases of practical interest, however, are small.