Abstract-A successful grasp of an object can be guaranteed when the object can never escape from the surrounding fingers during the entire grasping execution. Ability to capture an object clearly contributes to the robustness and success of grasping tasks. Object concavity is a useful geometric property allowing objects to be captured with only few fingers. In particular, certain concave objects may be captured using two fingers by appropriately placing the fingers close to some pair of opposite concave sections. Based on this intuitive idea, we address the problem of capturing concave polygonal objects with two disc-shaped fingers. We present an approach for computing a range of distance such that the two fingers can move away from a given immobilizing grasp but still prevent the object from escaping; when within this computed range, it is guaranteed under the frictionless contact assumption that the fingers can move toward each other to bring the object to the given immobilizing grasp. The proposed approach is implemented and preliminary result is presented.