An elastic spherical shell is compressed between two parallel rigid plates and undergoes large geometrical deformation. The convex surface conforms and adheres to the plates. The shell profile and contact stresses under large deformation are obtained numerically using a finite difference method. A thermodynamic energy balance following the classical Johnson-Kendall-Roberts (JKR) model is established to construct the adhesion mechanics, such that the sum of potential energy of the external load, elastic energy stored in the elastic shell, and surface energy to create new surface is minimized. Interrelationship between applied load, approach distance, contact radius, and deformed profile, as well as the "pull-off'' phenomenon, are derived. A comparison is made between this model and existing models for a solid sphere in the literature.