Based on a novel contact-space formulation, this paper presents a new algorithm to find two-fingered caging grasps of planar polygonal objects. We show that the caging problem has several useful properties in contact space. First, the critical points of the cage representation in the hand’s configuration space appear as critical points of an inter-finger distance function in contact space. Second, the critical points of this distance function can be simply characterized. Third, the contact space admits a rectangular decomposition where the distance function is convex in each rectangle, and all critical points lie on the rectangle boundaries. This property leads to a natural “caging graph,” which can be readily searched to construct the caging sets. An example, constructed from real-world data illustrates and validates the method.