The problem that is addressed here is that of a circular thin plate clamped peripherally with frictionless contact to an elastic sphere. A complete and effective solution to this problem is developed to describe the relationship between the contact force and the relative penetration. Analysis of the contact stress and surface displacements of the plate and the sphere is carried out. Comparison of the results with the Hertz theory indicates that the former predicts relative penetration with more accuracy, which indicates that the Hertz theory is not applicable to the elastic sphere in contact with the circular thin plate with a large deformation. In addition, the results of the theoretical model show good agreement with the ANSYS simulation results.