The higher audio frequencies are becoming of great interest in vibration studies, due to structure-borne noise considerations. In the uniform beam-column structures described, meaningful results are obtained when shear, rotary-inertia, and impedance terminations and corner joints are included. A distributed analysis is obtained using a multipole matrix representation of each beam-column section, containing transcendental functions as matrix elements. This is a generalization of the four-pole matrix used for distributed electrical or acoustical transmission lines. Beam bending in two principal planes is given by the Timoshenko beam equations, allowing shear and rotary-inertia effects. Axial elongation and torsion of each section are included. Several examples are discussed. The sidesway excitation of a plane frame composed of three I-beams with 90° corners shows important effects due to beam shear and corner flexibility. A simple three-dimensional frame composed of three equal beam elements and 90° corners correlates almost exactly with experimental results for at least ten modes of vibration, limited only by experimental techniques. Here, effects of torsion and elongation of the beam elements were significant. Impedance and response curves, resonant frequencies, and mode shapes are shown for these examples.