It is well known that aerodynamic forces acting on an elastic lifting surface are affected by structural deformations caused by aerodynamic forces on the surface or changes of attack angle due to these deformations. This type of problems are referred to as aeroelastic problems. Aeroelastic effects are much more significant in aerodynamic performance of yacht sails than ordinary wings of aircrafts, because the sail of yacht is formed by an elastic membrane. The pressure distribution on a membrane in a flow can be calculated if the shape of the membrane is determined. However, the shape is a result from the equilibrium of aerodynamic pressure and inner stress of the membrane, which depends on aerodynamic pressure. In order to treat this kind of mutual interaction between aerodynamic forces and elastic forces, some analytical or numerical approaches have been proposed to give reasonable solutions. In the present paper, Finite Element Method and a modified Vortex Lattice Method are adopted to solve aeroelastic problems of 3-dimensional elastic membrane sails. Made is use of large deformation incremental method to calculate stress and strain in deformed state of membranes, and to determine the sail shape in equilibrium state under loadings. One of the main advantages of the incremental method is that this method can be applied to dynamic problems more easily than the iterative method. The usefulness of this approach is confirmed by comparing numerical results obtained by the present method with existing numerical solutions of elastic membranes and experimental results of yacht sails as well. As examples of application of the solution proposed in this paper, a series of numerical calculation is carried out to clarify the effect of leech tension and sail material on the aerodynamic performance of sail.