Unsteady Navier-Stokes computations have been carried out for simulating transonic flows over a clipped delta wing undergoing oscillatory and ramp motions, including flexibility. The implicit upwind algorithm has been validated by comparing the solutions with experimental data for the oscillatory pitching motion cases. The numerical and experimental results agree well at moderate angles of attack, where a leading-edge vortex develops. The ramp motion cases have demonstrated the effects of unsteadiness of the flowfleld and structural flexibility on the wing responses. For the 10-deg ramp motion, a vortex breakdown is observed. The inviscid interaction with the shock wave plays an essential role in the process of the breakdown observed in the present calculation.