<p>The dynamic impedances (including stiffness and damping) of bucket foundations play a key role in influencing the dynamic behaviour of bucket-supported offshore wind turbines (OWTs). This study presents a rigorous elastic solution for the dynamics of laterally loaded bucket foundations. Firstly, accurate closed-form formulae are obtained for frequency-dependent lumped and distributed springs and dashpots. The spring stiffness coefficients decrease with increasing load frequency. The spring damping coefficients primarily depend on the bucket foundation aspect ratios and are not significantly affected by the load frequency. Subsequently, the corresponding frequency-independent spring-dashpot-added mass model coefficients are obtained to facilitate engineering applications. The added masses are also primarily related to the bucket aspect ratio. The dynamic responses obtained using the different models are then compared, and the results demonstrate that the responses of wind turbines can be accurately predicted using the frequency-independent spring-dashpot-added mass model. The spring plays a governing role in the low-frequency range, while the dashpot plays an important role in the medium-frequency range, especially near the resonant frequencies of OWTs, and the added mass starts to play a significant role at high frequencies.</p>