In this paper we are concerned with the application of the stabilized finite element method to aero-elastic problems. The main attention is paid to the numerical solution of incompressible viscous two dimensional flow around a
flexibly supported solid body. Typical
velocities in this case are low enough to assume the air flow being incompressible, on the other hand the Reynolds numbers are very high ($10^4-10^6$). As the neccessary mesh refinement for standard Galerkin approximation is clearly unfeasible, several possibilities of stabilization procedures (SUPG - streamline upwind/Petrov-Galerkin, GLS - Galerkin Least Squares) is discussed. Moreover the application of the stabilized method to an aeroelastic problem is presented.