  We analyze the structure of singularities, Mordell-Weil lattices and torsions
of a rational elliptic surface using string junctions in the background of 12
7-branes. The classification of the Mordell-Weil lattices due to Oguiso-Shioda
is reproduced in terms of the junction lattice. In this analysis an important
role played by the global structure of the surface is observed. It is then
found that the torsions in the Mordell-Weil group are generated by the fraction
of loop junctions which represent the imaginary roots of the loop algebra $\hat
E_9$. From the structure of the Mordell-Weil lattice we find 7-brane
configurations which support non-BPS junctions carrying conserved Abelian
charges.
