This study reports static and dynamic aeroelastic analyses of an aircraft wing in an incompressible flow. A swept thin-walled composite beam with a biconvex cross-section is used as the structural model that incorporates a number of non-classical effects such as material anisotropy, transverse shear deformation and warping restraint. A symmetric lay-up configuration i.e. circumferentially asymmetric stiffness (CAS) is further adapted to this model to generate the coupled motion of flapwise bending-torsion-transverse shear. For this beam model, the unsteady aerodynamic loads are expressed using Wagners function in the time-domain as well as using Theodorsen function in the frequency-domain. The divergence and the flutter speeds are evaluated for several ply angles and the aeroelastic response of an aircraft wing exposed to gust load is examined. The effects of transverse shean fiber-orientation and sweep angle on the aeroelastic instabilities and the aeroelastic response of the beam are further discussed.