Sheet metal parts with high-quality surface have wide applications in many manufacturing procedures. However, polishing these parts are challenging due to occurrence of deformations at contact area between the polishing tool and part. This stems from the thinness of these parts, making them susceptible to deformations, compared to thick solid parts. To address the above challenge, this study proposes a new robotic polishing path planing method that accounts for such deformations. The proposed method starts by estimating the contact area between the tool head, and the free-form surface of the sheet metal part is estimated using Hertz theory and differential geometry. Next, it uses a polynomial equation—that is derived from FEM-based contact analysis of the part—to calculate the true tool-part contact area under deformations. Then, it combines the contact-area information with a new constant speed robot path planing technique to ensure high-quality robot polishing. Numerical studies on several sample geometries verify the effectiveness of the method.