Exerting a force on a mechanical system can induce mechanical instability. To overcome that instability, humans may take advantage of their upper limb mechanical impedance (e.g., hand stiffness). The authors investigated what stiffness is required to maintain static stability and how humans can achieve that stiffness in the context of the task of pushing on a pivoting stick. Results showed that the stiffness required is in the range of measured human upper limb stiffness. To avoid an ill-posed problem, one can better express the requirements for stability as a simple geometrical criterion related to the curvature of the potential energy field at the hand. A planar model of the upper limb revealed that individuals can use both hand rotational and translational stiffness to stabilize a stick. Although hand rotational stiffness does not participate in producing the axial force on the stick, it can significantly contribute to achieving a limb stiffness appropriate for maintaining static stability. Hand rotational stiffness can be important for the design of hand tools, because humans can increase it only by augmenting grip force, a biomechanical factor associated with cumulative trauma injuries of the upper extremities.