A numerical solution is presented for a single load-unload cycle of an adhesive contact between an elastic-plastic sphere and a rigid flat. The interacting forces between the sphere and the flat. are obtained through connecting nonlinear spring elements having force-displacement behavior that obeys the Lennard-Jones potential. Kinematic, rather than isotropic, hardening is assumed for the sphere material to account for possible secondary plastification during the unloading. The well-known Tabor parameter and a plasticity parameter are shown to be the two main dimensionless parameters governing the problem. The effects of these two parameters on the load-approach curves, on the plastically deformed sphere profiles, and on the plastic strain fields inside the sphere are presented, showing different modes of separation during the unloading. (C) 2008 Elsevier Inc. All rights reserved.