This paper reports on an investigation of the relationship between the polishing force and the contact characteristics as the polishing tool approaches the boundary of a part surface during polishing. It was previous established that, for fixed abrasives, when the polishing tool is on the inner surface, the relationship between the polishing force and the pressure at the contact is approximately Hertzian and the contact is a full ellipse. The contact cannot be a full ellipse as the tool touches the boundary. The same polishing force could yield rather different pressure distribution, and thus rate of material removal, within the contact region. A model is proposed to relate the force and the pressure distribution as the tool is close to the edge of a part surface. The model takes into account changes of the contact near the edge. Experimental results are also presented to validate the proposed method.