The present paper investigates the flow induced dynamics of a non-linear fluid-structure interaction (FSI) system comprising of a symmetrical NACA 0012 airfoil supported by non-linear springs. Two methods are used in calculating the aerodynamic loads: a linear analytical approach and a full Navier-Stokes (N-S) solution. The analytical approach is based on the assumption of potential flow theory and a rigid wake. Wind velocity as a bifurcation parameter shows that the structural response undergoes a supercritical Hopf bifurcation. However, the analytical loads predict unrealistic bifurcation onset at low values of solid to fluid added mass ratio (μ) relevant to the application of flapping wing micro air vehicles (MAVs), showing the extremely large amplitude of oscillations. These observations render the use of an inviscid approach meaningless at such parametric regimes. Hence, we propose to use a N-S solver to emphasize the limit of applicability of the linear aerodynamic theory. Moreover, the inclusion of the viscous effects can potentially result in interesting dynamical behavior that has not been captured by the analytical approach. A bifurcation and stability analysis has been carried out for different parametric variations of μ in the fluid structure interaction system. © 2016 The Authors.