A foundational framework for functionally graded, doubly curved sandwich structures is presented. The theory is based on a comprehensive non-linear formulation that incorporates two types of material gradation. It adopts a first-order shear deformation approach, which offers a balance between simplicity and accuracy, with only a minor compromise in precision. The governing equations are derived using an energy-based method. This theoretical model accounts for the effects of edge loads, lateral loads, and surface tractions.