Analyzed is the mutual deformation of adhesive particles that interact with van der Waals forces using a viscoelastic theory that accounts for the time dependence of the phenomenon. The particle shape and interaction is calculated self-consistently for finite-ranged forces. Typical loading-unloading trajectories display hysteresis that increases with driving velocity, as does the particles' adhesion. An analytic approximation that accounts for the precontact deformation is tested against the exact numerical benchmarks and found to be accurate.