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The effect of bending buckling of carbon nanotubes (CNTs) on thermal conductivity of CNT materials is investigated in atomistic and mesoscopic simulations. Nonequilibrium molecular dynamics simulations of the thermal conductance through an individual buckling kink in a (10,10) single-walled CNT reveal a strong dependence (close to inverse proportionality) of the thermal conductance of the buckling kink on the buckling angle. The value of the buckling kink conductance divided by the cross-sectional area of the CNT ranges from 40 to 10 GWm-2 K-1 as the buckling angle changes from 20 to 110°. The predictions of the atomistic simulations are used for parameterization of a mesoscopic model that enables calculations of thermal conductivity of films composed of thousands of CNTs arranged into continuous networks of bundles. The results of mesoscopic simulations demonstrate that the conductivity of CNT films is sensitive to the angular dependence of the buckling kink conductance and the length of the individual CNTs. For a film composed of 1 µm-long CNTs, the values of the in-plane film conductivity predicted with a constant conductance of 20 GWm-2 K-1 and the angular-dependent conductance obtained in atomistic simulations are about 40 and 20% lower than the conductivity predicted for the same film with zero thermal resistance of the buckling kinks, respectively. The weaker impact of the angular-dependent buckling kink conductance on the effective conductivity of the film is explained by the presence of a large fraction of kinks that have small buckling angles and correspondingly large values of conductance. The results of the simulations suggest that the finite conductance of the buckling kinks has a moderate, but non-negligible, effect on thermal conductivity of materials composed of short CNTs with length up to 1 µm. The contribution of the buckling kink thermal resistance beco- es stronger for materials composed of longer CNTs and/or characterized by higher density of buckling kinks.