The paper considers the problem of parametric synthesis of design solutions at the stage of preliminary aerodynamic design of an advanced supersonic transport (SST) under epistemic uncertainty. To solve such a problem, optimization models were developed with objective functions and constraints depending on the input and optimizable uncertain parameters, information on which is formed on the basis of expert estimates. The non-deterministic representation of such parameters is formed on the basis of the uncertainty theory by Dr Baoding Liu (Tsinghua University, China), which provides low computational complexity for a wide range of objective functions and constraints at the stage of preliminary aerodynamic design. With the use of the developed non-deterministic optimization models, typical problems of the synthesis of SST design parameters under epistemic uncertainty are formulated and solved.