Functional activity of a protein molecule depends on a subtle balance between its flexibility and rigidity. We have demonstrated that the difference in the folding rates for proteins displaying similar folding topologies with similar compactness of 3D structures can be explained by different rigidity of protein molecules: the more rigid proteins have faster kinetics. The FoldUnfold program has been used to find flexible regions in protein chains. Monte-Carlo simulations for proteins with ferredoxin-like fold and proteins belonging to homeodomain-like superfamily demonstrate that the obtained refolding time values correlate reasonably well with the experimental data and such difference in the folding times can be explained by a different number of residues in flexible regions in the considered protein structures.