In this paper, unsteady thin aerofoil theory is extended to the case of two interacting aerofoils that oscillate harmonically perpendicular to the direction of the incident flow. The two aerofoils represent the headsail and mainsail of a yacht that sails upwind in waves. The developed theory is validated against theoretical data from the literature and results from wind tunnel tests with rigid, high-aspect ratio sail models oscillating at reduced frequencies from k = 0 to k = 0.68. Good agreement is found between the predicted and measured chordwise pressure distributions. An application of the theory to the case of an International America's Cup Class yacht reveals that the time-varying components of the aerodynamic forces are small and that the thrust gain is minimal, i.e. only very little energy can be extracted from the unsteady flow about the sails. No attempt is made to investigate the influence of the flexibility of the sails, three-dimensional effects or phenomena related to dynamic stall.