Unique elastic fields, beams defined by a given set of orthonormal scalar functions on a two-dimensional or three- dimensional beam manifold, are treated. The proposed approach enables one to obtain sets of orthonormal beams and various families of localized fields in both isotropic and anisotropic solids. This can be applied also to sound beams in liquids. By way of illustration, the fields defined by the spherical harmonics are considered. The families of orthonormal beams can be used as functional bases for complex elastic fields. The obtained localized elastic fields include storms, whirls, and tornadoes, i.e., the localized fields for which time average energy flux is identically zero at all points, azimuthal, and spiral, respectively. It is shown that these fields can be combined into a complex field structure, such as an ultrasonic diffraction grating. This makes them promising tools to control laser radiation.