The three-dimensional problem of the sound wave scattering by a compact obstacle of a general form in an Uflyand-Mindlin plate is considered. A formula that expresses the scattering field in terms of the analytic continuation of the directivity pattern is derived, and the formulas that describe the coupling of the scattering channels and allow the calculation of the surface wave amplitudes from the residues of the directivity pattern are obtained. For the case of nonradiating obstacles, the uniqueness of the solution to the scattering problem in the absence of absorption is established. An example of a localized shear wave is presented.