The Bernoulli-Euler theory of transverse beam vibration, suitably extended to take into account internal damping, has been used to derive closed-form expressions for the driving-point impedance and force transmissibility of three types of nonuniform cantilever beams: (1) those of rectangular section with constant breadth and a depth of increasing or decreasing linear taper, (2) those of rectangular section with linearly tapered depth and a breadth appropriately varied to maintain constant cross-sectional area, and (3) those with three discontinuous stages of arbitrary but uniform cross section. In each case, the beams are driven at their free end by a sinusoidally varying point force, and the frequency dependence of their impedance and transmissibility has been calculated. Representative results are presented for internal beam damping of the solid type for which the Young's modulus and associated damping factor are independent of frequency. The mass and length of the beams have been held constant and the graphical results compared in terms of the wavenumber of an equally massive reference beam of uniform section. [Investigation sponsored jointly by the U. S. Naval Ordnance Systems Command, the U. S. Naval Ship Systems Command, and the U. S. Office of Naval Research.]