  We study with semi-analytical methods the statistics of pronounced arcs
caused by lensing of galaxies by foreground galaxy clusters. For the number
density and redshift distribution of rich clusters we use Press-Schechter
theory, normalized on the basis of empirical data. For the background sources
we make use of observational results in the Hubble Deep Field. We present
results for three different lens models, in particular for the universal
profile suggested by Navarro, Frenk and White. Our primary concern is the
dependence of the expected statistics on the cosmological parameters,
$\Omega_M$, $\Omega_\Lambda$. The theoretical estimates are compared with the
cluster arcs survey EMSS, and the resulting constraints in the $\Omega$-plane
are presented. In spite of considerable theoretical an observational
uncertainties a low-density universe is favored. Degeneracy curves for the
optical depth and likelihood regions for the arc statistics in the
$\Omega$-plane depend only weakly on the cosmological constant.
