The structural damping effect on the flutter boundary has been investigated for three types of wings: rectangular, swept-forward, and swept-back. The unsteady aerodynamic loadings on oscillating wings are evaluated by the doublet-point method. The structures of the composite wings are modelled by the shear deformable finite element. The interpolation between the structural and aerodynamic grids is accomplished by using the surface spline. The effects of the composite fiber orientation on the natural frequency and the modal loss factor are studied for the rectangular and swept-back wings. Also, the effects of the fiber orientation on the flutter/divergence characteristics are investigated for the three types of wing. The structural damping of composite material gives the increase of the flutter speeds and the decrease of the flutter frequencies.