The formation tendency of monoatomic chains (MCs) of materials under tensile stress is considered in terms of a ratio between Peierls stress of a bulk crystal having dislocations and the theoretical break shear stress of a monoatomic chain. It is found that the metallic elements having the largest Poisson's ratio (v) and face centered cubic (fcc) crystalline structure hold the largest MC forming ability since they have the smallest elastic energy storage within the crystals and can thus endure the largest plastic deformation. According to the size, sequence of v of metallic fcc elements, the MC formation ability of these elements is predicted, which is in agreement with the available experimental and theoretical results.