Extragalactic gravitational lens systems are sensitive to the cosmological parameters Omega(M) and Omega(Lambda) through the angular size-redshift relation. When only a single background object (a "source") is being lensed, the cosmological information is hopelessly obscured by the unknown details of the lens mass distribution. However, when multiple sources over a range of redshifts are lensed, the cosmological information is in principle recoverable. In this paper we discuss a technique for extracting cosmological parameters from these multiple-arc systems and prospects for applying the technique to real systems.