Although acoustics is one of the disciplines of mechanics, its ”geometrization” is still limited to a few areas. The Reissner beam is one of the simplest acoustical system that can be treated in the context of mechanics with symmetry. It seems that the non-linear phenomena can be handled in their intrinsic qualities through the concepts of differential geometry. Using the symmetry of Lie groups, the geometric constructions needed for reduction are presented in the context of the ”covariant” approach.