  A complete catalogue of galaxy cluster models can be used to constrain
cosmological parameters like $\sigma_8$, the amplitude of the initial density
fluctuation spectrum. We focus here on two strong lensing statistics for
clusters of galaxies: the fraction of rich Abell clusters that are critical to
lensing, and the abundance of arcs in such clusters, especially the X-ray
luminous ones. The specific aim of this paper is to constrain $\sigma_8$ for
the standard Cold Dark Matter scenario within an Einstein-de Sitter universe.
