The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil inserted in a channel (e.g. wind tunnel). A solid airfoil with two degrees of freedom can rotate around the elastic axis and oscillate in the vertical direction. The numerical simulation consists of the finite element soluton of the Navier-Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. High Reynolds numbers up to 106 require the application of a suitable stabilization of the finite element discretization. Numerical results are compared with an experiment. and Obsahuje seznam literatury