We model the cluster lens MS 2137-23 in which Fort et al. (1992) found a tangential arc, a radial arc, and some arclets. We show that by only using observational constraints given by the CCD images we can model the two arcs and predict the positions of the three arclets. These successful results give strong confidence on the structural and dynamical parameters of the cluster found. In particular, the core radius of the cluster is small, probably 3 times smaller than the value generally adopted. The amount of dark matter is large with a mass-to-light ratio of about 100 and a line-of-sight velocity dispersion of 1000 km s^-1^. MS 2137-23 is the first case of a cluster lens in which we have enough distorted multiple images to really infer the distribution of dark matter in these systems. Therefore its study should be a first priority in the near future. Moreover, since the model is based on the assumption that the elongated radial structure is a radial arc, it is now urgent to get its redshift.