Offshore wind turbine (OWT) is a typical example of a slender engineering structure founded on large diameter rigid piles (monopiles). The natural vibration characteristics of these structures are of primary interest since the dominant loading conditions are dynamic. A rigorous analytical solution of the modified SSI eigenfrequency and damping is presented, which accounts for the cross coupling stiffness and damping terms of the soil–pile system and is applicable but not restrictive to OWTs. A parametric study was performed to illustrate the sensitivity of the eigenfrequency and damping on the foundation properties, the latter being expressed using the notion of dimensionless parameters (slenderness ratio and flexibility factor). The application of the approximate solution that disregards the off diagonal terms of the dynamic impedance matrix was found to overestimate the eigenfrequency and underestimate the damping. The modified SSI eigenfrequency and damping was mostly affected by the soil–pile properties, when the structural eigenfrequency was set between the first and second eigenfrequency of the soil layer. Caution is suggested when selecting one of the popular design approaches for OWTs, since the dynamic SSI effects may drive even a conservative design to restrictive frequency ranges, nonetheless along with advantageous – from a designers perspective – increased damping.