The paper considers the problem of determining parameters of the aerodynamic configuration and power plant of an advanced supersonic passenger transport (SST) at the stage of preliminary aerodynamic design under epistemic uncertainty associated with incomplete information about the initial data. Optimization models and algorithms based on them are proposed that operate with the designed SST initial parameters generated by experts on the basis of empirical prediction. Such parameters are proposed to be generated within Liu’s uncertainty theory as uncertain quantities expressed by uncertainty distribution functions. The use of uncertainty theory will make it possible to formalize and perform aerodynamic design process by replacing the functions that depend on uncertain quantities with their numerical characteristics. Such numerical characteristics are effectively interpreted by the decision maker, since they have analogues in probability theory – expected value, quantile, variance. The use of uncertainty theory in solving optimization problems under uncertainty provides low computational costs compared to the theory of probability. The paper discusses the use of numerical methods in the proposed algorithms, since, additionally, it is required to solve the black box function optimization problem. This is due to the lack of simple analytical relations between the SST requirements and the SST aerodynamic configuration and power plant parameters. The adequacy of the developed algorithms is demonstrated by the aerodynamic predictions presented by the Pareto fronts of the objective functions, which allow choosing trade-off design solutions.