α-helix and β-hairpin are the two principal secondary structures in proteins. A large number of experimental and theoretical kinetics and thermodynamics studies of the folding and unfolding of α-helix and β-hairpin structured polypeptides and proteins have been performed. Different theoretical models have been proposed to explain their folding mechanisms. Inconsistencies exist among the various models, which essentially reflect the different understanding of how individual structural elements affect the folding process and stability of protein structures. The present review mainly summarizes our recent simulation studies of the structure stability, folding and unfolding (denaturation) mechanism of various α-helix bundle and β-structure systems.