Binding of monovalent and divalent cations to two adenine-adenine platform structures from the Tetrahymena group I intron ribozyme has been studied using continuum solvent models based on the generalised Born and the finite-difference Poisson-Boltzmann approaches. The adenine-adenine platform RNA motif forms an experimentally characterised monovalent ion binding site important for ribozyme folding and function. Qualitative agreement between calculated and experimental ion placements and binding selectivity was obtained. The inclusion of solvation effects turned out to be important to obtain low energy structures and ion binding placements in agreement with the experiment. The calculations indicate that differences in solvation of the isolated ions contribute to the calculated ion binding preference. However, Coulomb attraction and van der Waals interactions due to ion size differences and RNA conformational adaptation also influence the calculated ion binding affinity. The calculated alkali ion binding selectivity for both platforms followed the order K(+) > Na(+) > Rb(+) > Cs(+) > Li(+) (Eisenman series VI) in the case of allowing RNA conformational relaxation during docking. With rigid RNA an Eisenman series V was obtained (K(+) > Rb(+) > Na(+) > Cs(+) > Li(+)). Systematic energy minimisation docking simulations starting from several hundred initial placements of potassium ions on the surface of platform containing RNA fragments identified a coordination geometry in agreement with the experiment as the lowest energy binding site. The approach could be helpful to identify putative ion binding sites in nucleic acid structures determined at low resolution or with experimental methods that do not allow identification of ion binding sites.