Ab initio molecular dynamics simulations are performed on small single wall nanotubes. By structural relaxation,the equilibrium C-C bond lengths and bond angles are determined. Our result shows that for both zigzag and armchair nanotubes there are two nonequivalent bond lengths. One bond stretches from that of the graphene sheet, while the other shrinks. Small variations on bond angles are also shown. Energy bands are calculated for the optimized structures. It is found that the intrinsic curvature of the very small nanotube greatly modifies the energy band which can no longer be well described in the tight-binding zone-folding picture. In our calculation very small nanotubes are metallic. The energy per atom fits quite well with the relation of E(R) = E0 + f/R2 even for the extreme small radius. The implications of the results on the properties of small nanotubes are discussed.