The unravelling of (10, 10) and (18, 0) single-walled carbon nanotubes (SWCNTs) is simulated using molecular dynamics simulations at different temperatures. Two different schemes are proposed to simulate the unravelling; completely restraining the last atom in the chain and only restraining it in the axial direction. The forces on the terminal atom in the unravelled chain in the axial and radial directions are reported till the separation of the atomic chain from the carbon nanotube structure. The force-displacement relation for a chain structure at different temperatures is calculated and is compared to the unravelling forces. The axial stresses in the body of the carbon nanotube are calculated and are compared to the failure stresses of that specific nanotube. Results show that the scheme used to unravel the nanotube and the temperature can only effect the duration needed before the separation of some or all of the atomic chain from the nanotube, but does not affect the unravelling forces. The separation of the atomic chain from the nanotube is mainly due to the impulsive excessive stresses in the chain due to the addition of a new atom and rarely due to the steady stresses in the chain. From the simulations, it is clear that the separation of the chain will eventually happen due to the closing structure occurring at the end of the nanotube that would not be possible in multiwalled nanotubes.