DNA and RNA are very important biological molecules. Both are highly negativelycharged. Positively-charged ions can bind to them through electrostatic interactions. The interaction between DNA (or RNA) molecules is affected by these ions. In this research, we investigate the physical mechanism of ion-mediated inter-DNA and interRNA interactions using a variety of X-ray techniques and other analytical tools. In our experiments, we focus on the property of short strand (20 or 25 base pair) DNA and RNA due to their great potential in novel therapeutic applications. The major experimental technique involved in this research is Small Angle X-ray Scattering (SAXS). We explore this method to measure interactions between freely-moving nucleic acids in solution. We demonstrate the impact of positively-charged ions on the interactions between short double-stranded DNA (or RNA) molecules through a series of experiments and theoretical models. The valence of the ion ranges from divalent (Mg2+), trivalent (such as cobalt hexamine and cobalt sepulchrate) to tetravalent (spermine). The results show that not only ionic strength but also the valence, size and hydration level of the ions as well as geometry of nucleic acids play important roles in the inter-nucleic acid interaction. This research provides insight into the physical mechanism of like-charge attraction and establishes the physical basis of DNA (or RNA) packaging achieved by small ions.