The adhesion of particles is modeled with finite element analysis using an energy approach comparable with that used in the JKR formalism. The strain energy of a cylindrically symmetric system, comprising a particle adhering to a surface with a fixed contact size, is computed as a function of contact size and then added to an energy term that is linearly proportional to the contact patch area. These computations also include contributions from the potential energy of a body force comparable with that which might be applied by a centrifuge. The results show regions of stability (adhesion) where a local energy minimum exists and regions of release where separation of the particle from the surface leads to a continuous decrease in the energy of the system. The effect of the deformation of the particle is included implicitly as a result of the FEM which provides details of the strains and stresses within the system. Discussion concentrates on the physical meaning of the behaviors and the significance of JKR-like theories that use an effective surface energy to represent electrostatic and van der Waals contributions to the adhesion. Modeling the effects of surface roughness of particles and the plastic deformation of particles through an effective surface energy is considered.