There is an increasing interest in the secondary structure of beta-amino-acid-containing peptides, since these compounds exhibit an intrinsic propensity to form stable folds even for short peptides, a feature that is rarely observed in alpha-amino-acid-containing peptides. In this work, we use a multiple trajectory molecular dynamics approach to study a panel of cyclic beta-amino-acid-containing peptides with a variety of motifs that differ in the ring size, ring substituents, and terminal protecting groups. We find a reasonable agreement between the predicted and the experimentally observed structures, in spite of the simple solvent representation used, indicating that in most cases the folding proceeds energetically downhill and it is driven to a great extent by structural preferences coded in the internal degrees of freedom, a result supported by our energy partition analysis. Our results also show that when the N-terminal end is unprotected, it is likely to be charged in a protic polar solvent. In that case, we find that only a molecular dynamics simulation with an "all atom" solvent representation is capable of reproducing the experimentally observed secondary structure of the peptide. Finally, the time evolution analysis of the hydrogen-bond-induced turns as well as of the root-mean-square deviation from the observed structure indicates that some peptides could have a higher intrinsic flexibility than others, within a given fold, a result that correlates to some degree with our molecular mechanics energy analysis.