This paper investigates the interaction between two rigid spheres and between a rigid sphere and a rigid half-space, based on the Lennard-Jones potential. By using the divergence theorem and integrating the Lennard-Jones potential over the surfaces, the analytical forms of the surface tractions were obtained, and by integrating the Lennard-Jones potential over the volumes, the analytical form of the total force between two rigid spheres was obtained. The results are compared to those with the Derjaguin approximations and with the parabolic approximation for the sphere profile. The accuracy of the Derjaguin approximation and the parabolic approximation were estimated. The analytical surface traction can be used for the adhesive contact between an elastic body and a rigid one. (C) Koninklijke Brill NV, Leiden, 2012