This paper presents a novel model for workpiece positioning analysis. Existing fixturing models may underestimate the positioning error due to neglect of the curvature of one or both contacting bodies. By using surface-to-surface signed distance function, a two-sided quadratic model for fixture locating analysis is developed. A system of quadratic sensitivity equations, which relate locators’ source errors to the resulting workpiece localization error, are derived. The second-order geometric properties of both workpiece and locators are taken fully into account. The present model is more accurate than the existing linear model and one-sided quadratic model, which is verified through numerical examples. It has potential applications in fixture design, fault diagnosis, and tolerance analysis.