The criteria necessary to determine the optimal fresh water production equipment design are presented in the doctoral thesis. The existing methods, the shape and the consumption of energy in the process of operation are analyzed. Additional criteria used for the selection of both the stationary and the marine fresh water producing equipment, are given as well. The mathematical models describing the processes that occur during vacuum distillation, the method most commonly in use on board large ships, are developed, as well as the models of the sea water thermodynamic properties depending on the temperature and the salinity. Furthermore, the processes of a continuous evaporation and of evaporation in charges have been analyzed, which led to the development of the mathematical model of fresh water producing equipment capacity dependence on the exploitation terms. The two and three dimensional diagrams showing changes of the salt concentration in the water, i. e. salinity, during the distillation process are given. The mathematical model of the capacity dependence on the exploitation terms, i. e. the sea water salinity and its entry temperature, the quantity of the heating energy and, the vacuum in the vessel, allows further considerations on the marine engineer optimal behavior or, the optimal design of the distillation equipment control system. The validity of the model has been confirmed through the poll method and by comparing it with the engine room simulator of one of the world most distinguished producer. The exploitation terms changes have been simulated thus confirming, by a set mathematical model, its influence on the equipment, namely the capacity and the distillate salinity. Besides the equipment capacity model, the application of the automatic control system has been analyzed, which resulted in the two suggested models. In the first case, it is a fully automated plant, while the second case represents a slightly simplified version with fewer elements but completely in accordance with the equipment capacity mathematical model.