The present study aims to explore the buckling responses of T-carbon nanobeams and nanoplates by molecular dynamics simulations. The AIREBO potential has been used. The critical buckling force and critical axial strain are reported for various nanostructures. The effects of the length, width-to-thickness ratio, and temperature on the buckling behavior have been investigated. The results show that for T-carbon nanobeams, by increasing the length at a constant temperature, the critical force and critical strain decrease, while by increasing temperature, the critical force increases, and the critical strain decreases. Furthermore, for T-carbon nanoplates, as the width-to-thickness ratio is increased at a constant temperature, the critical force increases but the critical strain decreases, and by increasing temperature, the force increases but the strain decreases. Moreover, it is observed that by increasing the strain rate, the critical buckling force rises slightly. The findings of our research help to gain a general understanding of the buckling behavior of T-carbon nanostructures, which is useful for their future designs and applications.