Flexible and conformal positioning of the skin is of great significance for the efficient and low deformation assembly of aircraft panels. As the main conformal positioning part of the skin, the fixture positioning surface is complicated to design when taking into account the flexible positioning. In this study, taking the low deformation and flexible clamping of the skin under complex stress conditions as the target, a fixture positioning profile design method is proposed to predict the deformation of the skin and provide moderate support for the skin based on thin plate theory (TPT). In the face of complex stress and boundary conditions of the skin, the differential method is used to solve the stress and deformation of the skin under different support conditions, which is correctly verified by finite element simulation. The proposed method reveals the influence of the fixture positioning profile on the deflection of the aircraft skin under concentrated load (drilling force), which provides a good design theoretical basis for the fixture design for the low deformation flexible clamping of the skin.