Topological defects (TDs) arise in the growth process of two-dimensional (2D) materials, as well as after-growth heat treatment or irradiation. Our atomistic simulation results show that their mechanical modulation of material properties can be understood qualitatively through the theory of elasticity. We find that the in-plane lattice distortion and stress induced by experimentally characterized pentagon-heptagon (5|7) pairs or pentagon-octagon-pentagon (5|8|5) triplets can be captured by 2D models of dislocations or disclinations, although the out-of-plane distortion of the lattice reduces stress localization. Lineups of these TDs create nonlocal stress accumulation within a range of ∼10 nm. Interestingly, pileups of 5|7 and 5|8|5 defects show contrasting tensile and compressive buildups, which lead to opposite grain size dependence of the material strength. These findings improve our understandings of the mechanical properties of 2D materials with TDs, as well as the lattice perfection in forming large-scale continuous graphene films.