Existing aeroelastic analyses for finite wings have been mostly limited to cases with a steady freestream. In reality, however, the inflowing freestream can often be unsteady and pulsating. Therefore, this paper presents unsteady aerodynamic and aeroelastic analyses for a finite wing under a pulsating freestream. A new three-dimensional unsteady vortex lattice model under a pulsating freestream has been developed in discrete-time domain to examine unsteady aerodynamic forces acting on a vibrating wing. The structural behavior of the wing has been analyzed using a three-dimensional plate model. An aeroelastic model is then constructed by coupling the unsteady aerodynamic model with the structural model. Since the freestream velocity is assumed to be time-varying, the flutter onset of a wing under pulsating freestream is predicted by Floquet analysis. Numerical results of an untwisted and untapered wing show that the new time domain method can predict the aeroelastic stability as well as time history of the isolated wing under a pulsating freestream.