The conformational study on L-azetidine-2-carboxylic acid (Ac-Aze-NHMe, the Aze dipeptide) and (S)-piperidine-2-carboxylic acid (Ac-Pip-NHMe, the Pip dipeptide) is carried out using ab initio HF and density functional methods with the self-consistent reaction field method to explore the differences in conformational preferences and cis-trans isomerization for proline residue and its analogues with different ring size in the gas phase and in solution (chloroform and water). The change of ring size by deleting a CH2 group from or adding a CH2 group to the prolyl ring results the remarkable changes in backbone and ring structures compared with those of the Pro dipeptide, especially in the C'-N imide bond length and the bond angles around the N-C(alpha) bond. The four-membered azetidine ring can have either puckered structure depending on the backbone structure because of the less puckered structure. The six-membered piperidine ring can adopt chair and boat conformations, but the chair conformation is more preferred than the boat conformation. These calculated preferences for puckering are consistent with experimental results from analysis of X-ray structures of Aze- and Pip-containing peptides. On going from Pro to Aze to Pip, the axiality (i.e., a tendency to adopt the axial orientation) of the NHMe group becomes stronger, which can be ascribed to reduce the steric hindrances between 1,2-substituted Ac and NHMe groups. As the solvent polarity increases, the polyproline II-like conformation becomes more populated and the relative stability of conformation tC with a C7 hydrogen bond between C'=O of the amino group and N-H of the carboxyl group decreases for both the Aze and Pip dipeptides, as seen for the Pro dipeptide. The cis population and rotational barriers for the imide bond increase with the increase of solvent polarity for both the Aze and Pip dipeptides, as seen for the Pro dipeptide. In particular, the cis-trans isomerization proceeds in common through only the clockwise rotation with omega' approximately +120 degrees about azetyl and piperidyl peptide bonds in the gas phase and in solution, as seen for alanyl and prolyl peptide bonds. The pertinent distance d(N...H-N(NHMe)) and the pyramidality of imide nitrogen can describe the role of this hydrogen bond in stabilizing the transition state structure, but the lower rotational barriers for the Aze and Pip dipeptides than those for the Pro dipeptide, which is observed from experiments, cannot be rationalized.