All-atom molecular mechanical (MM) force field parameters are developed for a cyclic beta-amino acid, amino-cyclo-pentane-carboxylic acid (ACPC), using a multi-objective evolutionary algorithm. The MM model is benchmarked using several short, ACPC-containing alpha/beta-peptides in water and methanol with SCC-DFTB (self consistent charge-density functional tight binding)/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the tetra-alpha/beta-peptide in water. For the octa-alpha/beta-peptide in methanol, the MM and SCC-DFTB/MM simulations predict the 11- and 14/15-helical form as the more stable conformation, respectively; however, the two helical forms are very close in energy (2-4 kcal/mol) at both theoretical levels, which is also the conclusion from recent NMR experiments. As the first application, the MM model is applied to an alpha/beta-pentadeca-peptide in water with both explicit and implicit solvent models. The stability of the peptide is sensitive to the starting configuration in the explicit solvent simulations due to their limited length ( approximately 10-40 ns). Multiple ( approximately 20 x 20 ns) implicit solvent simulations consistently show that the 14/15-helix is the predominant conformation of this peptide, although substantially different conformations are also accessible. The calculated nuclear Overhauser effect (NOE) values averaged over different trajectories are consistent with experimental data, which emphasizes the importance of considering conformational heterogeneity in such comparisons for highly dynamical peptides.