The transonic small disturbance (TSD) equation is used for the aeroelastic analysis of vertical and horizontal tail of aircrafts. TSD code has been developed for the aeroelastic analysis of swept vertical surfaces. The steady aerodynamic results of TSD code are verified from those of Euler and CAP-TSD codes in subsonic, transonic and supersonic regions. The unsteady aerodynamic results are also compared with those of CAP-TSD code. Aeroelastic analyses of vertical and horizontal tail of aircrafts have been performed in the time domain using computational fluid dynamics (CFD) and computational structural dynamics (CSD) for symmetric and anti-symmetric modes. The structural coordinates are interpolated into the aerodynamic coordinates using surface infinite plate theory. The damping ratio and frequency of aeroelastic responses are estimated by the exponential sine fitting method to determine the flutter speed. From the results of present study, it is shown that the anti-symmetric mode is more unstable than the symmetric mode.