Present paper has investigated the effects of the structural damping on flutter boundary for two types of wing: rectangular and swept-back wings. The unsteady aerodynamic loadings on oscillating wings are evaluated by the doublet-point method. The structure of composite wing is modelled by the transverse shear deformable finite elements. The interpolation between the structural and aerodynamic grids is accomplished by using the surface spline. The effects of the fiber orientation of the modal loss factors 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 two types of wing. The addition of the structural damping increases the flutter speeds and decreases the flutter frequencies.