We have studied the relative stability of narrow-finite length Carbon nanotubes and nanostrips as a function of their length. We find that the critical radius (∼2 Å) for tube stability is independent of the length of the tubes and equals the critical radius of infinite length tubes. The independence of the critical radius on chirality is also established. We have also investigated the thermal stability of short nanotubes and nanostrips by performing extensive molecular dynamics simulations. The strips exhibit a higher thermal stability than the tubes even in those cases when they are structurally less stable. The thermal decomposition temperature (∼1000 K) of the tubes comes out in good agreement with the experiments.