This thesis deals with the optimization and selection of propulsion plants for liquefied natural gas tankers in a methodological and comprehensive way. It also includes a detailed analysis and comparison of operating costs for each propulsion plant alternative. Furthermore, the paper presents the influence of ship capacity, distance, propulsion power, the price of fuel and gas, the type of fuel used and the efficiency of main and auxiliary machinery within the propulsion plant on the total cost per year for each propulsion plant alternative. The results of the mathematical models of non-linear polynomial function set out the functional and statistical dependence of the total cost of a propulsion plant (operating costs and fuel costs) with reference to propulsion power, the price of heavy fuel oil and diesel oil, natural gas price and efficiencies of the main and auxiliary machinery at different voyage distances and different ship capacities. The results of the mathematical models of non-linear polynomial function (from the fifth grade polynomial function to the linear regression) with total cost as the dependent variable and all other variables as the independent variables show that all models give high-quality approximation so that the deviation between the actual values and the regression values is negligible. The resulting mathematical models allow simple insight into the total cost of a propulsion plant and enable a quality selection of the optimal propulsion plant for a liquefied natural gas tanker using four or five basic parameters without the knowledge of the other possibly less important parameters that have influence on the total cost. The mathematical models offer a faster and better scientific method for propulsion plant optimization and selection. Optimizing the process of selection and management of the propulsion plant ultimately reduces the total cost of the propulsion plant and the scientifically based procedure allows a quality selection of a propulsion plant for a liquefied natural gas tanker. Finally, the results reduce the business risk and increase the effect of shipowners’ business performance.