Many polycrystalline metal aggregates display a slight amount of anisotropy due to texture that develops during fabrication procedures such as rolling. This macroscopic anisotropy produces a birefringence of SH-waves propagating normal to the plate, i.e., the velocity of SH-waves polarized parallel to the rolling direction is usually faster than that of SH-waves polarized perpendicular to the rolling direction. For polarization angles not in or perpendicular to the rolling direction the wave is assumed to split into two waves, one polarized parallel and one polarized perpendicular to the rolling (similar to what is observed for particular propagation directions in single crystals). However slightly anisotropic materials have only a small percentage of preferential grain alignment, the bulk of the grains being of random orientation. In consideration of these materials being nearly isotropic, having slight anisotropy superimposed, and the possibility of multiple textures, we address the energy distribution of SH-waves as a function of polarization angle with respect to the material symmetry axes and the transducer orientation. The importance of considering attenuation in this work is also addressed.