In order to characterize the contact force of robotic grinding with special-shaped discs with small pointed tips and significant base pressure difference, the work aims to propose a modeling method to calculate the grinding contact force of the robotic special-shaped disc considering the flexural deformation of the thin plate and the elastic deformation of the rubber disc within a two-layer structure. Firstly, the relationship between contact force and the flexural deformation of the thin plate was analyzed based on the theory of thin plates. Furthermore, according to the static elastic theory, the elastic deformation and contact force model of rubber plate in the elastic deformation region was established. Then, the finite element numerical simulation was conducted to explore the elastic deformation parameters of the rubber disc and the flexural deformation parameters of the thin plate. By employing the variable substitution, a numerical inverse function model of the contact force in relation to the normal feed displacement of the special-shaped disc was derived. Finally, a robotic experimental platform dedicated to special-shaped disc grinding was constructed. Validation experiments were performed on a flat workpiece and a workpiece with three different curved surfaces to verify the effectiveness of the contact force model across various workpiece shapes and surface curvatures. The results of these validation experiments confirmed that the contact force model accurately predicted the contact force, particularly when the disc inclination angle was significant. In the consistency verification experiments for robotic special-shaped disc grinding, it was observed that under identical grinding parameter conditions, the average grinding depth for the three different grinding paths was 0.066 3, 0.063 2, and 0.064 5 mm, respectively. The maximum deviations were 0.013 9, 0.009 0, and 0.010 8 mm, respectively. The coefficients of variation for each path were determined as 11.2%, 6.4%, and 9.6%, respectively. The experimental validation confirmed the effectiveness of the proposed method. The proposed method considers the morphological features of the special-shaped disc and incorporates parameters such as workpiece surface curvature, disc inclination angle, profile parameters, and disc dimensions into the grinding contact force model. It also describes the numerical inverse function relationship between the grinding contact force and the normal feed displacement of the special-shaped disc. This method enables the measurement of the contact region in special-shaped disc grinding operations and provides insights into the factors affects the grinding contact force. It serves as a theoretical basis for efficient and high-quality grinding with the constant contact force in robotic special-shaped disc grinding operations.