Existing offshore areas require development and mining using floating structures. The article presents design issues and settings of anchor mooring systems for marine floating structures. Improving and optimization methods for mooring systems, presented in publications of Russian and foreign authors, are discussed. The parameters influencing the safety of floating marine structures operation are identified. The parameters that are advisable to take as criteria are discussed. The restrictions imposed on non-criteria parameters are considered. The optimization criterion of the marine floating structures mooring systems in extreme operating modes is formulated. An optimization method for mooring systems is suggested in accordance with the proposed criterion. The study gives an example of mooring system optimization in the storm mode for a platform operated in ice-free seas. A similar methodology can be used for mobile ice-resistant platforms, conceptual variants of which are being developed for operation in Arctic conditions.  Research results were obtained by the method of mathematical modeling.