With the increasing demand for oil, oil companies have been forced to exploit new fields in deep waters. Due to the high cost of oil exploitation operations, the development of technologies capable of increasing efficiency and reducing costs is crucial. In this context, the use of floating units in deep waters has become more frequent. The positioning of the floating units during oil exploitation operations is done using mooring lines, which are flexible structures usually made of steel wire, steel chain and/or synthetic cables. This work presents the development of a Genetic Algorithm (GA) procedure to solve the problem of the mooring pattern of floating units used in oil exploitation operations. The distribution of mooring lines is one of the factors that directly influence the displacements (offsets) suffered by floating units when subjected to environmental conditions such as winds, waves and currents. Thus, the GA seeks an optimum distribution of the mooring lines whose final goal is to minimize the units´ displacements. The basic operators used in this algorithm are mutation, crossover and selection. In the present work, the steady- state GA has been implemented, which performs the substitution of only one or two individuals per generation. The computation of the floating unit´s static equilibrium position is accomplished by applying the catenary equilibrium equation to each mooring line in order to obtain the out-of-balance forces on the unit, and by using an iterative process to compute the final unit equilibrium position.