Liposome carriers for delivering small interfering RNA (siRNA) into target cells are of tremendous importance because the siRNA-based therapy offers a completely new approach for treating a wide range of diseases, including cancer and viral infections. In this paper, we employ the state-of-the-art computer simulations to get an atomic scale insight into the interactions of siRNA with zwitterionic (neutral) lipids. Our computational findings clearly demonstrate that siRNA does adsorb on the surface of a neutral lipid bilayer. The siRNA adsorption, being rather weak and unstable, is driven by attractive interactions of overhanging unpaired nucleotides with choline moieties of lipid molecules. It is the presence of the unpaired terminal nucleotides that underlies a drastic difference between siRNA and DNA; the latter is not able to bind to the zwitterionic lipid bilayer. We also show that adding divalent Ca ions leads to the formation of stable siRNA lipid system complexes; these complexes are stabilized by Ca-mediated aggregates of siRNA and lipid molecules rather than by the overhanging siRNA nucleotides. Furthermore, the molecular mechanism of interactions between siRNA and the lipid bilayer in the presence of divalent cations seems to involve exchange of Ca ions between the outer mouth of the major groove of siRNA and the lipid/water interface. Overall, our findings contribute significantly to a deeper understanding of the structure and function of liposome carriers used for siRNA delivery and can be used as a theoretical basis for further development of siRNA-based therapeutics.