AbstractEffective schemes exist to calculate aerodynamic forces for thin bodies and structural dynamics of flexible membranes. The fluid dynamic of thin wings in a irrotational flow leads to the lifting surface theory. Neglecting the inertia of the membrane the structural dynamics are solved by the non‐linear (FEM).But the interaction of flexible membranes and an irrotational flow causes problems due to the different nature of the mathematical equations. On the one hand, there is a partial differential equation for the structural dynamics and on the other hand, there is a singular integral equation for the aerodynamics. The numerical discretization scheme has to fit these different types of equation.Our work introduces a new interaction scheme to couple the singular integral equation of the lifting surface theory with the non‐linear FEM of the membrane static. The fundamental examinations, showed by Schoop et al. (International Journal for Numerical Methods in Engineering 1998; 41: 217–219), are applied to realistic sail geometries and the aerodynamics is extended to instationary flow conditions. Copyright © 2001 John Wiley & Sons, Ltd.