A continuum-based analysis for a pile floating in a homogeneous viscoelastic soil stratum is demonstrated. The soil displacement field in the vertical direction is expressed as a product of separable functions, and the effect of radial soil displacement is accounted through a modification of the soil modulus. The Extended Hamilton’s Principle is applied in which the kinetic energy, potential energy, and the work done by the external forces are expressed in terms of the soil displacement function. The differential equations governing pile and soil motions, and the motion of the cylindrical soil domain below the pile base are obtained along with the necessary boundary conditions, which are solved analytically in an iterative algorithm. The accuracy of the developed analysis is ensured with an existing solution in the literature. A parametric study is also conducted to examine the effect of stratum thickness, pile-soil stiffness ratio, pile-soil density ratio, Poisson’s ratio, and damping ratio on the axial pile-head stiffness with dimensionless frequency.