Abstract: Shock wave/boundary layer interaction (SWBLI) is a complex flow phenomenon frequently encountered during high-speed flight, which can induce flow separation and subsequent structural flutter, posing a severe threat to flight safety and aerodynamic performance. The nonlinear flutter of curved panels under SWBLI involves strong coupling between flow separation and large geometric deformation, yet a systematic fluid-structure interaction (FSI) understanding of this coupled system remains lacking. To reveal the underlying nonlinear aeroelastic mechanisms, a partitioned two-way FSI numerical model is established, coupling the unsteady compressible Navier-Stokes equations with the von Kármán nonlinear plate theory. The effects of the curvature coefficient and the shock impingement location on the aeroelastic response of a two-dimensional curved panel are systematically investigated. The results show that the curved panel exhibits a deformation pattern with opposite signs in the front and rear portions, and significant asymmetry relative to the shock impingement location: for convex curvature, the mean deflection is downward with the trailing-edge displacement about 6-7 times that of the leading edge, while for concave curvature, the mean deflection is upward with the leading-edge displacement about 4-5 times that of the trailing edge. As the curvature increases, the flow separation region lengthens and the flutter amplitude grows; specifically, as |H/h| increases from 0 to 5, the mean deflection at the 3/4 chord of the convex panel increases by 4 panel thicknesses, whereas that of the concave panel decreases by 1 thickness, and the concave panel consistently exhibits smaller mean deflection than the convex one. When |H/h| reaches 3, flutter vanishes and the system transitions to a fixed-point stable state. Furthermore, the influence of the shock impingement location is nonlinear: when the impingement point is near either end, the system converges to a fixed-point stable state, with faster convergence and smaller static deformation as the point moves further downstream; the maximum mean deflection and flutter amplitude occur when the shock impinges at the panel centre and decrease towards both ends. The critical impingement locations for flutter onset and termination are asymmetric about the mid-point, and the flutter parameter range shrinks by one-quarter when the impingement point shifts downstream. These findings can provide theoretical reference and data support for the aeroelastic design and flow control of curved-wall structures in high-speed vehicles.