Possible molecular conformations in peptide nanorings and nanotubes were theoretically investigated by a mathematical conformation analysis as well as ab initio Hartree-Fock calculations. The mathematical analysis predicts not only the conventional nanorings having an extended-type (E-type) backbone (trans zigzag) but also the novel ones having bound-type (B-type) backbones with a smaller internal diameter. Ab initio calculations for the amino acid substitution reveal that all 20 encoded residues can form both types of the above nanorings as a local minimum. However, the energetically stable type is determined in accordance with the kind of the replaced side chains. Moreover, the present work theoretically reveals that both types of nanorings stack to form nanotubes through inter-ring hydrogen bonds, i.e., larger E-type nanotubes and smaller B-type nanotubes. Electronically, the HOMO and LUMO states of the nanoring and nanotube backbones are formed by the in-plane a state. The replacement by the appropriate residues is furthermore predicted to intrude additional levels in the energy gap and to form the frontier states localized at the side chains.