We present the first strong-lensing study of the mass distribution in the cluster MS 2053-04 based on HST archive data. This massive, X-ray luminous cluster has a redshift z=0.583 and is composed of two structures that are gravitationally bound to each other. The cluster has one multiply imaged system composed of a double gravitational arc. We have performed a parametric strong-lensing mass reconstruction using NFW density profiles to model the cluster potential. We also included perturbations from 23 galaxies, modeled like elliptical singular isothermal spheres, that are approximately within 1'×1' around the cluster center. These galaxies were constrained in both the geometric and dynamical parameters with observational data. Our analysis predicts a third image that is slightly demagnified. We found a candidate for this counterimage near the expected position and with the same F702W-F814W colors as the gravitational arcs in the cluster. The results from the strong-lensing model show the complex structure in this cluster, the asymmetry and the elongation in the mass distribution, and are consistent with previous spectrophotometric results that indicate that the cluster has a bimodal mass distribution. Finally, the derived mass profile was used to estimate the mass within the arcs and for comparison with X-ray estimates.