A numerical method to compute the nonlinear Fluid-Structure Interactions (FSI) of yacht sails is presented in this paper. The inviscid lifting-line flow model is used by including a quadrature method to efficiently compute sail pressure loads. The structural calculation is performed with a quasi-static resolution by using a dynamic backward Euler scheme, in order to improve the computation convergence. A specific thickness sail approach is also proposed to make the FSI solving easier. The assembly of these flow and structural methods leads to a fast and robust strategy to compute nonlinear FSI on yacht sails, and the proposed approach is applied on a complex semi-rigid composite mainsail.