For the design of sailing vessels, the use of Dynamic Velocity Prediction Programs is expanding, as naval architects start to consider the effects of waves and varying wind conditions in order to design faster, safer and more efficient vessels. Many models that predict the unsteady hydrodynamic response are available, but for sail aerodynamics, few models have been presented, and the quasi-steady assumption is instead commonly used. The aim of this paper is to develop a time-domain model for unsteady sail aerodynamics that can handle arbitrary motions and requires only limited input. The proposed model is based on the Indicial Response Method, with specific adaptations to handle the additional complexity of sail aerodynamics. The model’s predictive performance is evaluated against URANS CFD results for several cases of increasing complexity. This includes a 3D upwind sail plan subjected to pitching motion, where comparisons are also made with the common quasi-steady (Q-S) assumption. Compared to this, the proposed model delivers significantly better predictions for the amplitude of lift, thrust and sideforce. However, the drag amplitude is over-predicted by the model, and as a result, there is a significant misprediction of thrust phase. While there is a need to improve the prediction of unsteady drag, this paper shows that the model represents a significant improvement over the Q-S assumption, for unsteady performance prediction on timescales shorter than the wave period.