As an alternative to gravity footings or pile foundations, offshore wind turbines at shallow water can be placed on a bucket foundation. The present analysis concerns the development of consistent lumped-parameter models for this type of foundation. The aim is to formulate a computationally efficient model that can be applied in aero-elastic codes for fast evaluation of the dynamic structural response of wind turbines. The target solutions, utilised for calibration of the lumped-parameter models, are obtained by a coupled finite-element/boundaryelement scheme in the frequency domain, and the quality of the models are tested in the time and frequency domains. It is found that precise results are achieved by lumped-parameter models with two to four internal degrees of freedom per displacement or rotation of the foundation. Further, coupling between the horizontal sliding and rocking cannot be disregarded without significant loss of accuracy. Finally, special attention is drawn to the influence of the skirt stiffness, i.e. whether the embedded part of the caisson is rigid or flexible.