The longitudinal oscillations of tapered visco-elastic bars are considered. The analytical technique used is a generalization of the classical theory of acoustic horns, and a brief review of knowledge to date of this subject is first presented. The analysis provides an assessment of the damping effects on propagating waves and standing wave modes. Taper shapes treated include the following: exponential; catenoidal; inverse catenoidal; sinusoidal; inverse sinusoidal; Gaussian; power-law. For visco-elastic rods the dependence of the wavenumber and decay factor on frequency and damping is shown graphically in dimensionless form for several of these rod geometries.