Within the identification of the prevailing frequencies in a coupled soil-pile-structure system, a pseudo-natural SSI frequency is defined as the frequency where pile-head motion is minimized with respect to both free-field and structural motion. This frequency is determined analytically and the proposed solution is compared to numerical results from finite-element analyses for a single-degree-of-freedom structure supported on a single end-bearing pile. The role of foundation vibration modes on pseudo natural-to-effective natural SSI frequency ratio and effective damping of the coupled system is explored, as affected by salient model parameters such as relative stiffness and inertia between structure and soil, foundation flexibility and pile slenderness. It is observed that for stiff massive structures founded on a stiff and/or short pile, pseudo-natural frequency may deviate substantially from the conventional effective natural frequency, providing a possible design frequency associated with lower levels of pile radiation damping. Conversely, when a flexible tall structure is supported on a flexible pile for which foundation rocking prevails, pseudo-natural frequency and conventional effective natural frequency nearly coincide regardless of the superstructure mass, allowing prediction of the actual flexible-base vibrational characteristics of a SSI system even in the absence of free-field recordings.