The Peierls-Hubbard model applied to N-membered ring-shaped molecules is investigated numerically and analytically. The bond configurations minimizing the total energy at half-filling of the electronic states are determined by a self-consistent method for N less than or equal to 8 in a wide range of the electron-lattice and electron-electron coupling parameters. In the even-N case, only dimerized and homogeneous configurations have been found to be stable. Odd-N rings show three types of bond configurations depending on the coupling parameters. Two of these configurations have reflection symmetry whereas the third one is irregular.(C) 1999 American Institute of Physics. [S0021-9606(99)30630-9].