The formulation and quality of a computationally efficient model of offshore wind turbine surface foundations are examined. The aim is to establish a model, workable in the frequency and time domain, that can be applied in aeroelastic codes for fast and reliable evaluation of the dynamic structural response of wind turbines, in which the geometrical dissipation related to wave propagation into the subsoil is included. Based on the optimal order of a consistent lumped-parameter model obtained by the domain-transformation method and a weighted least-squares technique, the dynamic vibration response of a 5.0 MW offshore wind turbine is evaluated for different stratifications, environmental conditions and foundation geometries by the aeroelastic nonlinear multi-body code HAWC2. Analyses show that a consistent lumped-parameter model with three to five internal degrees of freedom per displacement or rotation of the foundation is necessary in order to obtain an accurate prediction of the foundation response in the frequency and time domain. In addition, the required static bearing capacity of surface foundations leads to fore-aft vibrations during normal operation of a wind turbine that are insensitive to wave propagating in the subsoil-even for soil stratifications with low cut-in frequencies. In this regard, utilising discrete second-order models for the physical interpretation of a rational filter puts special demands on the Newmark beta-scheme, where the time integration in most cases only provides a causal response for constant acceleration within each time step. (C) 2014 Elsevier Ltd. All rights reserved.