The fluid induced vibration (FIV) phenomena of a 2-D.O.F airfoil system have been investigated in low Reynolds number incompressible flow region. Unsteady flows with viscosity are computed using two-dimensional incompressible Navier-Stokes equations. To validate developed Navier-Stokes code, steady and unsteady flow fields around cylinder and airfoil are analyzed and the results are compared with experiment and previous computations. The present fluid/structure interaction analysis is based on the most accurate computational approach with computational fluid dynamics (CFD) and computational structural dynamics (CSD) techniques. The highly nonlinear fluid/structure interaction phenomena due to severe flow separations have been analyzed for the low Reynolds region ($R_N$=500~5000) that has dominant flow viscosity. The effect of $R_N$ on the flutter (fluid/structure coupled vibration instability) boundary of 2-DOF airfoil system is presented and the effect of initial angle of attack on the dynamic instability is also obtained.