Carbon nanotubes (CNTs) are known to possess extraordinary strength, stiffnessand ductility properties. Their fracture resistance is an important issue from theperspective of durability and reliability of CNT-based materials and devices.According to existing studies, brittle fracture is one of the important failure modesof single-walled carbon nanotube (SWNT) failure due to mechanical loading.However, based on the authors’ knowledge, the fracture resistance of CNTs has notbeen quantified so far. In this paper, the fracture resistance of zigzag SWNTswith preexisting defects is calculated using fracture mechanics concepts basedon atomistic simulations. The interatomic forces are modelled with a modifiedMorse potential; the Anderson thermostat is used for temperature control. Theproblem of unstable crack growth at finite temperature, presumably caused by thelattice trapping effect, is circumvented by computing the strain energy release ratethrough a series of displacement-controlled tensile loading of SWNTs (appliedthrough moving the outermost layer of atoms at one end at constant strain rate of9.4 × 10−4 ps−1) with pre-existing crack-like defects of various lengths. The strain energy release rate,G, is computed for (17, 0), (28, 0) and (35, 0) SWNTs (each with aspectratio 4) with pre-existing cracks up to 29.5 Å long. The fracture resistance,Gc, is determined as a function of crack length for each tube at threedifferent temperatures (1, 300 and 500 K). A significant dependence ofGc on crack length is observed, reminiscent of the risingR curve behaviour of metals at the macroscale: for the zigzag nanotubesGc increases with crack length at small length, and tends to reach a constant value ifthe tube diameter is large enough. We suspect that the lattice trapping effectplays the role of crack tip plasticity at the atomic scale. For example, at 300 K,Gc for the (35, 0) tube with aspect ratio 4 converges to6 J m−2 as the cracklength exceeds 20 Å. This value is comparable with the fracture toughness of graphite and silicon. The fractureresistance of the tubes is found to decrease significantly as the temperature increases. Tostudy the length effects, the computations are repeated for zigzag nanotubes with the samethree chiralities but with aspect ratio 8 at 1 K. The fracture resistances of thelonger nanotubes are found to be comparable to those of the shorter nanotubes.