It is well known that dishing occurring in chemical mechanical polishing of plug structures leads to considerable wafer surface non-planarity and reduces the current/charge conduction. Thus, a closed-form solution for quantitative prediction of dishing is needed. A contact-mechanics-based approach to describe the steady-state dishing occurring in chemical mechanical polishing of plug structures is presented. The model is then applied to investigate the effect of pattern geometry on dishing in details. It was shown that plug dishing strongly depends on plug size, but minimally on pattern density. In addition, the maximum value of dishing occurs at a critical pattern density for fixed pitch.