Two-dimensional allotropes of group-IV substrates including silicene, germanene and stanene have recently attracted considerable attention in nanodevice fabrication industry. These materials involving the buckled structure have been experimentally fabricated lately. In this study, first-principles density functional theory calculations were utilized to investigate the mechanical properties of single-layer and free-standing silicene, germanene and stanene. Uniaxial tensile and compressive simulations were carried out to probe and compare stress-strain properties; such as the Young's modulus, Poisson's ratio and ultimate strength. We evaluated the chirality effect on the mechanical response and bond structure of the 2D substrates. Our first-principles simulations suggest that in all studied samples application of uniaxial loading can alter the electronic nature of the buckled structures into the metallic character. Our investigation provides a general but also useful viewpoint with respect to the mechanical properties of silicene, germanene and stanene.