The bending behavior of a curved sandwich panel with a transversely flexible core, i.e. “soft” in the out of plane direction, is derived. It is formulated using a rigorous systematic closed-form approach based on variational principles. The effects of the transversely flexible core are incorporated resulting in non-linear patterns, denoted also as high-order effects, for the inplane and the transverse deformations through the height of the core. The governing equations along with the associated boundary and continuity conditions for a general type of sandwich panels, i.e. unidentical skins, composite laminated or metallic and a “soft” core are derived. General type of boundary conditions, including spring conditions, as well as different conditions at the upper and the lower skins at the same section are implemented and the effects of “stiff edge inserts, denoted as global boundary conditions, along with the induced localized effects are considered. Localized effects at support regions with or without edge stiffeners, with movable and immovable supports, and in the vicinity of concentrated loads are studied. The effects are described in terms of the internal resultants and displacements of each skin, peeling (transversely normal) stresses and shear stresses at the skin-core interfaces, and stress and displacement fields in the core through its height. Numerical results of a typical curved panel used in a test set-up and comparisons with experimental data are presented. A comparison, that is in very good agreement, between the analytical results and the experimental ones is conducted. The effects of a global boundary conditions, such as a “stiff” edge beam, and similar local boundary conditions on the localized effects are presented and discussed. The stress concentration involved in case of a concentrated load especially in its near vicinity is described.