This paper presents a new mathematical approach for the analysis of a harmonically vibrating, linear, elastic, tapered pile. The soil consists of a number of horizontal elastic strata that are homogeneous, isotropic, and linearly viscoelastic. The governing differential equation for an arbitrary pile segment is obtained and solved. The solution starts from the pile toe and ends up with the pile head. It will be shown that when the taper angle is increased, the resonant amplitudes of piles decrease. It will also be demonstrated that the resonance amplitudes and resonant frequencies of the floating tapered pile and a uniform pile of the same volume and length vary slightly. However, the resonant amplitude of an end-bearing tapered pile is significantly less than that of the equivalent uniform pile. It will generally be concluded that the use of tapered piles subjected to axial harmonic vibrations is superior to the use of cylindrical piles of the same length and volume. This is very attractive for dynamically loaded piles, encouraging the practical use of tapered piles.