The Bernoulli‐Euler theory of transverse beam vibration, suitably extended to take into account internal beam damping, is used to derive closed‐form expressions for the mechanical driving‐point impedance and force transmissibility of two types of nonuniform cantilever beams that are driven at their free ends by a sinusoidally varying point force. The beams are truncated and of rectangular cross section; they have a linearly tapered depth and have either (1) constant breadth or (2) parabolically varying breadth. Representative computations of the frequency dependence of impedance and transmissibility are plotted for beams having the same length and mass as an equally long and equally massive uniform reference beam. Significant attenuation or amplification of force transmissibility is observed, depending on the proportions of the beams and on whether their depth tapers towards their fixed or free end. The measured resonance frequencies of a set of nonuniform aluminum (6061‐T651) cantilever beams agree closely with the predictions of theory.