Abstract In this paper, we present the spatial and planar force-displacement relationships which characterize individual contacts on a fixtured workpiece. The compliance at each contact is modeled and expressions for the changes in contact forces as a function of the rigid body relative motion between the fixture elements and the workpiece are developed for three-dimensional fixtures. Using these relationships, the stable fixturing of planar workpieces is demonstrated for material-removal operations. By example, we first describe how to choose the clamp geometry so the overall movement of the workpiece is minimized and then determine the “best” two-contact clamping arrangement using a quality measure based on the deviation from the nominal part dimensions.