  We investigate the potentiality of using strong lensing clusters to constrain
the cosmological parameters Omega_m and Omega_lambda. The existence of a
multiple image system with known redshift allows, for a given (Omega_m,
Omega_lambda) cosmology, absolute calibration of the total mass deduced from
lens modelling. Recent Hubble Space Telescope (HST) observations of galaxy
clusters reveal a large number of multiple images, which are predicted to be at
different redshifts. If it is possible to measure spectroscopically the
redshifts of many multiple images then one can in principle constrain
(Omega_m,Omega_lambda) through ratios of angular diameter distances,
independently of any external assumptions. For a regular/relaxed cluster
observed by HST with 3 multiple image systems, each with different
spectroscopic redshifts, we show by analytic calculation that the following
uncertainties can be expected: Omega_m=0.30 +/- 0.11, Omega_lambda=0.70 +/-
0.23 or Omega_m=1.00 +/- 0.17, Omega_lambda=0.00 +/- 0.48 for the two most
popular world models. Numerical tests on simulated data confirm these good
constraints, even in the case of more realistic cluster potentials, such as
bimodal clusters, or when including perturbations by galaxies. To investigate
the sensitivity of the method to different mass profiles, we also use an
analytic ``pseudo-elliptical'' Navarro, Frenk & White profile in the
simulations. These constraints can be improved if more than 3 multiple images
with spectroscopic redshifts are observed, or by combining the results from
different clusters. Some prospects on the determination of the cosmological
parameters with gravitational lensing are given.
