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Graphyne is the allotrope of graphene. In this letter, four different graphynes (α, β, γ, and 6,6,12-graphenes) are investigated by molecular dynamics simulations to explore their mechanical properties and failure mechanisms. It is found that the presence of the acetylenic linkages in graphynes leads to a significant reduction in fracture stress and Young’s modulus with the degree of reduction being proportional to the percentage of the linkages. This deterioration in mechanical properties stems from the low atom density in graphynes and weak single bonds in the acetylenic linkages where the facture is initiated.