Due to a high demand for offshore wind energy the industry is expanding to evermore challenging locations such as seismic prone areas. The corresponding seismic shocks and vibrations can be transmitted to jack‐up vessels and their cranes used for the installation of these offshore wind turbines. Since a potential collapse due to seismic activity carries large human and financial risks, the main objective of this thesis is: ”To determine the best solution to mitigate the dynamic response of cranes for offshore wind turbine installation in seismic prone areas.” Therefore, we study existing mitigation measures and find that the dynamic absorber and base isolation systems are promising solutions. However, we only find the dynamic absorber to be feasible for implementation. Subsequently, we investigate the influence of the dynamic absorber on the dynamic response of the crane by performing seismic time history analyses. We find a mitigating influence for the vast majority of simulated cases. More specifically, the dynamic response in the out‐of‐plane direction is reduced by 10 percent on average. Furthermore, the dynamic absorber is highly effective in the mitigation of harmonic vibrations such as those that are induced by Rayleigh waves that occur near the end of earthquakes. This finding suggests that a dynamic absorbers might also be suitable for mitigating wave and wind loads in the crane as these loads prescribe a rather harmonic signal. The conclusions of this thesis give the offshore wind industry a clear indication that a dynamic absorber is an effective measure to mitigate the dynamic response of a crane that is based on a jack‐up.