The role of facial vibrissae (whiskers) in the behavior of terrestrial mammals is principally as a supplement or substitute for short-distance vision. Each whisker in the array functions as a mechanical transducer, conveying forces applied along the shaft to mechanoreceptors in the follicle at the whisker base. Subsequent processing of mechanoreceptor output in the trigeminal nucleus and somatosensory cortex allows high accuracy discriminations of object distance, direction, and surface texture. The whiskers of terrestrial mammals are tapered and approximately circular in cross section. We characterize the taper of whiskers in nine mammal species, measure the mechanical deflection of isolated felid whiskers, and discuss the mechanics of a single whisker under static and oscillatory deflections. We argue that a tapered whisker provides some advantages for tactile perception (as compared to a hypothetical untapered whisker), and that this may explain why the taper has been preserved during the evolution of terrestrial mammals.