A numerical model for the simulation of the fluid-structure interaction (FSI) between the wind and the sails of a sailing boat is presented. This problem is characterized by an extremely light structure (in particular when downwind sails, spinnaker or gennaker, are considered) experiencing large displacements under the action of a complex (turbulent and separated) flow field. The model is based on a strongly coupled segregated FSI approach which guarantees adequate stability properties for the FSI problem at hand. A Dirichlet-Neumann coupling algorithm is adopted with a finite-volume Reynolds Averaged Navier-Stokes (RANS) flow solver interacting with a finite-element shell structural solver. Numerical results of unsteady FSI simulations are presented and discussed.