It is shown that the known solution of the acoustic scattering problem on a supported elastic plate, described by the Timoshenko model, should be corrected. The general formulation of the contact conditions that imply the reciprocity principle is given. Sommerfeld’s formula and the “optical” theorem for the model are formulated. They lead to the uniqueness of the solution. The numerical comparison of the effective cross section of scattering from supported elastic plate described by the Kirchhoff and by the Timoshenko models is presented.