In aero-elastic simulation of offshore wind turbines, the support structure can be modelled using an “integrated” approach, where the jacket and tower and modelled explicitly as one structural body, or a “superelement” approach, where the jacket part of the support structure is included as a superelement. For integrated modelling, vibration mode shapes are calculated for the whole support structure. For a superelement approach, separate mode shapes are defined for superelement and the tower. The different modal basis makes it difficult to align the structural damping definition for the two approaches, meaning that manual tuning of the modal damping ratios has previously been necessary to achieve equivalent damping on the whole support structure for the two approaches. To provide a consistent damping approach, it is proposed to specify modal damping ratios or Rayleigh damping on a modal basis which is common to the two approaches: the support structure natural mode shapes. When damping is specified on the natural modes of the support structure, equivalent support structure damping is observed for superelement and integrated modelling approaches. This allows the target support structure damping ratios to be achieved easily and also facilitates studies to compare the superelement and integrated modelling approaches.