The mechanical properties of graphyne nanostructures have been investigated by utilizing molecular dynamics simulation with AIREBO potential function. Results show that the numbers of acetylenic linkages between neighboring hexagonal rings have significant effects on the mechanical properties of graphyne and its derivatives. Anisotropic mechanical properties of these nanosheets and nanotubes are observed in uniaxial tensile tests. A mechanically strengthening-like behavior is presented in the stress–strain relationships of graph-n-yne (n= 3, 4, 5) nanotubes. A softening is presented in the stiffness-strain evolutions of nanostructures (n= 0, 1, 2) with a stiffening showing in nanostructures (n= 3, 4, 5). Furthermore, the fracture mechanism of nanostructures has also been discussed.