The structures and relative energies of all expected isomers and intermediates of new carbaporphyrin systems (2-aza-21-carba-23-X(thia or oxa)-porphyrin with or without 5,10,15,20-tetraphenyl) have been calculated using density functional theory (DFT) methods. The two tautomers having inside N-H turned out to be almost isoenergetic, with the relative energy difference less than 0.5-1.0 kcal/mol for both thiacarbaporphyrin and oxacarbaporphyrin. The tautomer having outside N-H is calculated to have only 1-3 kcal/mol higher energy than the lowest-energy isomer for the thiacarbaporphyrin, whereas the difference increases up to about 9-12 kcal/mol for the oxacarbaporphyrin system. The results explain why three isomers can coexist in the thiacarbaporphyrin, whereas only two isomers can be observed in the oxacarbaporphyrin. The calculated structures show that the relative stability of the isomers is not determined by the steric hindrance between two hydrogen atoms inside the core ring but by the degree of the pi-electron resonance of the core framework. The relative energy of the intermediate structure having two hydrogen atoms at the C(21) atom is calculated to be about 3-6 and 11-15 kcal/mol for thiacarbaporphyrin and oxacarbaporphyrin, respectively. The overall energy barriers of the tautomerism between the isomers with inside N-H are estimated to be 12-15 and 20-22 kcal/mol for thiacarbaporphyrin and oxacarbaporphyrin, respectively. The shape of the core cavity made by the four inside ligand atoms (C, N, X, and N) is almost regular square in the oxacarbaporphyrin systems but rectangular or rhombic in the thiacarbaporphyrin systems.