This paper presents closed-form expressions for the analysis of floating single piles subjected to vertically propagating harmonic P-waves. The foundation soil is treated as poroelastic medium, and can be either fully-saturated or nearly-saturated. We show that the existence of non-continuous air phase in the form of air bubbles dissolved in the pore water will have noteworthy effect on the vertical kinematic response of piles. Through parametric analyses we demonstrate that hydromechanical analysis techniques that consider soil as fully saturated may significantly over-estimate pile head displacements for frequencies relevant to seismic P-waves. In addition, we quantify differences in the response between end-bearing and floating piles, and show that these differences are more prominent when soil is not fully saturated. Although the proposed expressions have been derived while considering elastic soil and pile response, findings relevant to the effect of the degree of soil saturation to the vertical kinematic response of piles are generally applicable to any coupled stress-flow analysis method.