The subject of this paper is the numerical simulation of aeroelastic problems. The interaction of two-dimensional incompressible viscous flow and a vibrating airfoil is modelled. The solid airfoil, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The
numerical simulation consists of the finite element solution of the Navier-Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The stabilization procedure is of GLS type. The developed numerical approximation is applied on an aeroelastic problem.