Nonlinear aeroelastic computations are presented for a sweptback wing with underpylon/finned-store in the transonic and supersonic flow regions, where strong shock wave interactions exist. A modal-based coupled nonlinear aeroelastic analysis system with the matched-point concept has been developed using the high-speed parallel processing technique. Advanced numerical techniques such as computational structural dynamics and computational fluid dynamics are used. It is expected to provide accurate and useful engineering data in the aeroelastic and structural design of flight vehicles. For the nonlinear unsteady aerodynamics in high transonic flow region, Euler equations based on an unstructured grid system have been applied to consider fully the complex geometries. Linear and nonlinear aeroelastic computations have been conducted and are compared for the transonic and supersonic flow regions. Typically, it is shown that the advanced numerical approach gives much more conservative flutter boundary for the wing/pylon/store model than those predicted by the classical linear aerodynamic theories for high transonic flow. Also, important results indicate that in transonic flow the critical nonlinear flutter or limit-cycle oscillation-like phenomenon may be dominantly induced or within the bounds of strong possibility due to the shock coupling effect of unstable store induced vibration.