Mechanical deformations of nucleic acids (NA) play a very important role in many biological life processes. The bending persistence length of DNA is of specific interest, because so much eukaryotic DNA that stores genetic information is tightly packed inside cell nuclei, even though DNA is considered to be a relatively stiff biopolymer. However, recent experiments suggest that DNA may be more flexible than its persistence length (~ 150 bp or ~ 47 nm) suggests, especially for fragments shorter than 100 bp. It is important to reconcile these two seemingly competing pictures of DNA bending by providing a model that can explain the novel results without discrediting old experiments and the widely-accepted worm-like chain model. Another factor that influences both molecular geometry as well as mechanical properties is the ionic atmosphere surrounding the NA. It is known that multivalent ions with charge of +3e and higher can condense DNA into aggregates at high enough concentration. However, most conventional models cannot explain why RNA and DNA condense at different concentrations. Furthermore, our recent simulation results suggest that even though DNA persistence length decreases with multivalent ion concentration due to increasing electrostatic screening, RNA actually becomes stiffer due to a structural transition from the internal binding of the counterions.