[en] Highlights: • Mechanical properties of novel analogous of α-graphyne named α2-graphyne were studied. • The α-graphyne and α2-graphyne sheets are mechanically stable with stiffness. • These structures are proper materials for use in nanomechanical applications. The mechanical properties of two forms of graphyne sheets named α-graphyne and α2-graphyne under uniaxial and biaxial strains were studied. In-plane stiffness, bulk modulus, and shear modulus were calculated based on density functional theory. The in-plane stiffness, bulk modulus, and shear modulus of α2-graphyne were found to be larger than that of α-graphyne. The maximum values of supported uniaxial and biaxial strains before failure were determined. The α-graphyne was entered into the plastic region with the higher magnitude of tension in comparison to α2-graphyne. The mechanical properties of α-graphyne family revealed that these forms of graphyne are proper materials for use in nanomechanical applications.