This paper presents a framework to compute stable contact interfaces for automatically designing customized jigs used in bone surgeries. Given the surface model of a bone represented by polygonal meshes, we find out a small region on the surface to be used as the interface of a customized jig so that it can be stably fixed on the bone under a directional clamping force. The variation of directions on the clamping force is allowed in our formulation. Moreover, the surface region serves as the interface of stable contact must also be disassemblable so that the jig and the bone can be separated after removing the clamping force. The analysis of stable contact is formulated on a Gaussian map by the common regions of half-spaces according to the motion restrictions. A flooding algorithm is proposed to determine those disassemblable and stable contact interfaces on the surface of a bone, where the contact surfaces are later converted into the solid model of a jig to be fabricated by additive manufacturing. Experimental tests are taken to verify the stable contact between a bone and the jig generated by our approach.