The results of a detailed study of the effect of the cutout on the response of curved sandwich panels are presented. The panels have honeycomb core composite face sheets. The loading consists of a temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical sandwich panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities and their sensitivity to changes in the various panel, effective layer and micromechanical parameters.