Materials with negative longitudinal piezoelectric response have been a focus of recent research. So far, reported examples are mostly three-dimensional bulk materials, either compounds with strong ionic bonds or layered materials with van der Waals interlayer gaps. Here, we report the first example in two-dimensional elemental materials-the class of group-Va monolayers. From first-principles calculations, we show that these materials possess giant negative longitudinal piezoelectric coefficient e_{11}. Importantly, its physical mechanism is also distinct from all previous proposals, connected with the special buckling driven polarization in these elemental systems. As a result, the usually positive internal strain contribution to piezoelectricity becomes negative and even dominates over the clamped ion contribution in Bi monolayers. Based on this new mechanism, we also find several 2D crystal structures that may support negative longitudinal piezoelectricity. As another consequence, piezoelectric response in Bi monolayers exhibits a significant nonanalytic behavior, namely, the e_{11} coefficient takes sizably different values (differed by ∼18%) under tensile and compressive strains, a phenomenon not known before and helpful for the development of novel electromechanical devices.