By using DFT and semiempirical PM3 computational techniques, the electronic wave functions psi(n(l)) (k) at the states nearing the EF of some shortened (5,5) and (6,6) armchair nanotubes, on basis of optimized structure at B3LYP/6-31G level, have been studied. The calculated results found that the 0,(,) (k) have some regular periodic properties, mainly, no matter what diameter the nanotube is, their psi(n(l)) (k) can be repeated by the different periods at the short and long repeated cell directions respectively. An available and simple theoretical simulation method of research on the electronic structure and the quantum size effect of short armchair nanotubes is developed. The simulated results successfully reproduced the outcomes obtained from B3LYP or PM3 computational methods and STM experiments. (C) 2002 Published by Elsevier Science B.V.