During the manufacturing process of a rough workpiece, the non-uniformity of material mechanical properties can result in the generation of residual stresses within the workpiece, which can lead to structural failure. During the cutting removal process of the workpiece, the residual stresses gradually release, causing deformation. In this study, the "birth-death element" technique of finite element analysis was used to simulate the cutting removal process of the material. This process was then transformed into the release of residual stresses. A novel analytical method combining radial basis function interpolation with geometric and physical equations was proposed based on plate shell theory, small-deformation theory, theory of elasticity, and the superposition principle. The method aimed to invert the residual stress field and calculate the resulting deformation. This study was divided into two parts. In the first part, the influence of stress equilibrium equations was neglected, and the radial basis function interpolation method was used to invert the release of residual stresses in thin plates according to the initial residual stress field and the residual stress field after material removal. Next, the stresses were substituted into the physical equations to calculate the strain. The strain was then substituted into the geometric equations, and the plane displacement was calculated by strain integration from geometric equations. Based on the plate shell theory equations, the buckling deformation was inverted according to the plane displacement. In the second part, the reverse process of the first part was performed. Firstly, the buckling deformation caused by material removal in the thin plate was inverted. Then, the buckling deformation was substituted into the plate shell theory equations to invert the release of residual stress and the reconstructed residual stress field. The results demonstrated the reversibility of these two processes. Furthermore, the analytical solutions showed high agreement with the finite element solutions. This suggested that the analytical method proposed in this paper is applicable to thin-plate structures under elastic conditions and can be used to estimate residual stress distribution and predict deformation in the thin-plate cutting removal process.